on 22-Dec-2023 (Fri)

The general form of amplitude modulation of a signal \(s(t)\) is:

\(\displaystyle s_{HF}(t) = (A + \gamma s(t)) \cos(\omega_{c}t)\)

where \(A\) is the DC offset, \(\gamma\) is the AM sensitivity factor and \(\omega_{c}\) is the carrier angular frequency.

Using the Fourier Transform, Parseval’s theorem establishes a link between the energy of the time domain waveform and the energy of the spectrum: If \(x(t) \circ — \bullet X(j \omega)\), then \(\displaystyle \int_{-\infty}^{\infty}|x(t)|^2 d t=\frac{1}{2 \pi} \int_{-\infty}^{\infty}|X(j \omega)|^2 d \omega=\int_{-\infty}^{\infty}|X(f)|^2 d f\)

Using the Continuous-time Fourier series, Parseval’s Theorem for Periodic signal describes that the average power of a periodic signal is the sum of the average powers of its Fourier components: \(\displaystyle \frac{1}{T_{0}}\int^{T_{0}/2}_{-T_{0}/2}|x(t)|^{2}dt=\sum\limits^{\infty}_{k=-\infty}|C_{k}|^{2}\)

Wirth syntax notation (whole page)

Nix: Frst steps (whole page)

Other dyspnea-related chief complaints (eg, cough, chest discomfort) comprise an additional 9 percent of ED visits.

The most common diagnoses among older adult patients presenting to an ED with a complaint of acute shortness of breath and manifesting signs of respiratory distress (eg, respiratory rate >25, oxygen saturation [SpO₂] <93 percent) are decompensated heart failure, pneumonia, chronic obstructive pulmonary disease (COPD), pulmonary embolism (PE), and asthma [4].

Identify whether a life-threatening condition exists, such as:

• Acute coronary syndrome

• Acute heart failure

• Arrhythmia

• Pericardial tamponade

• Pulmonary embolism (PE)

• Pneumonia or other infection

• Chronic obstructive pulmonary disease (COPD) exacerbation

• Asthma

• Angioedema and anaphylaxis

• Poisoning (eg, carbon monoxide)

• Trauma (eg, pneumothorax, hemothorax)

Potential pitfalls in the approach of an acutely dyspneic emergency department patient include the following:

● Failure to secure the airway in a timely manner

● Failure to recognize and act on abnormal vital signs and signs of impending respiratory failure

● Over-reliance upon a single finding (physical examination or test result) to establish a diagnosis

● Failure to generate a proper differential diagnosis

● Failure to monitor the patient's clinical course

● Failure to consider carbon monoxide poisoning, methemoglobinemia, or PE

● Misinterpreting tachypnea, which may not represent a respiratory abnormality and may reflect nonpulmonary disease (eg, metabolic acidosis or impending herniation of the brainstem)

● Signs that portend imminent respiratory arrest include:

• Depressed mental status, which can occur with severe hypoxia or hypercarbia

• Inability to maintain respiratory effort (bradypnea, poor inspiratory effort, or agonal respirations)

• Cyanosis, which is uncommon and indicates severe hypoxia or methemoglobinemia

Signs suggestive of severe respiratory distress include:

• Retractions and the use of accessory muscles – Retractions occur with airway obstruction (eg, asthma, chronic obstructive pulmonary disease [COPD], foreign body) and can be seen in the suprasternal, intercostal, and subcostal areas [5]. They are an ominous sign suggesting extreme respiratory distress, fatigue of the respiratory muscles, and the potential for respiratory failure. Patients with neuromuscular disease may not manifest retractions due to muscle weakness, even in the face of severe respiratory compromise.

• Brief, fragmented speech (patient is unable to answer questions with anything more than a few words), which can be quickly assessed by asking the patient to count to 10 in one breath.

• Significant tachypnea (ie, greater than 25 breaths per minute). This cutoff is not absolute, and a respiratory rate of over 20 breaths per minute should prompt a timely evaluation.

• Inability to lie supine – Many patients in respiratory distress sit bolt upright or in a tripod position. An exception is hepatopulmonary syndrome, where patients may breathe more comfortably when recumbent. (See "Hepatopulmonary syndrome in adults: Prevalence, causes, clinical manifestations, and diagnosis", section on 'Dyspnea'.)

• Profound diaphoresis, which reflects extreme sympathetic stimulation associated with severe disease (eg, myocardial infarction, severe asthma flare, diastolic cardiac dysfunction).

• Audible stridor or wheezing, which can represent upper airway obstruction or severe bronchospasm.

• Dusky skin, which indicates poor perfusion or cyanosis.

• Agitation, somnolence, or other altered mental status in the dyspneic patient suggests severe hypoxia or hypercarbia. Patients with a depressed mental status from carbon dioxide (CO₂) retention may look comfortable and lackadaisical.

Provide supplemental oxygen – For hypoxic patients with respiratory difficulty, provide 50 to 60 liters per minute (LPM) of oxygen via a nonrebreather mask. To deliver this much oxygen, open the flow meter valve until the indicator lies well beyond the 15 LPM mark. An SpO₂ of 94 percent is an appropriate target for most patients.

Patients breathing 100% oxygen deliver five times as much oxygen to the alveoli per unit of ventilation as those breathing room air and, in the absence of parenchymal disease, can maintain a normal SpO₂ with only two or three breaths per minute. However, the best nonrebreather oxygen-delivery systems provide only 85% oxygen.

Continue focused history and examination – Assess for a potentially difficult airway and search for rapidly reversible causes (anaphylaxis, tension pneumothorax, pericardial tamponade, upper airway obstruction).

Optimize hemodynamic physiology – Control the rate or rhythm of a tachydysrhythmia and improve right ventricular filing pressures if needed (eg, IV fluids, vasopressors). When volume overload is suspected, can administer diuretics and/or preload and afterload reduction (eg, nitrates) depending on underlying physiology.

A venous blood gas may be useful in the assessment of the patient presumed to be somnolent from CO₂ retention. The partial pressure of carbon dioxide (PaCO₂) should be low in the acutely dyspneic patient, who is usually hyperventilating. A normal or elevated CO₂ in the setting of dyspnea and tachypnea portends respiratory failure.

Stroke – Although dyspnea is not the chief complaint of patients with an acute stroke, a number of respiratory abnormalities may result from a sufficiently severe injury or one affecting regions involved in respiration. Such abnormalities may include aspiration pneumonia, neurogenic pulmonary edema, and various abnormal respiratory patterns, including apnea.

Neuromuscular disease – Several neuromuscular diseases, including multiple sclerosis, Guillain-Barré syndrome, myasthenia gravis, amyotrophic lateral sclerosis, West Nile virus, and enterovirus D68 (seen primarily in children), can cause weakness of the respiratory muscles, leading to acute respiratory failure. Botulism may cause generalized descending muscle weakness involving the respiratory muscles.

Sepsis – Severe sepsis often causes respiratory compromise secondary to tachypnea and respiratory muscle fatigue, which may stem from underlying pneumonia, compensation for metabolic acidosis, or some other process.

Primary pulmonary disease – COPD, asthma, pneumonia, interstitial fibrosis, and others can lead to hypercapnic respiratory failure from hypoventilation, increased dead space, decreased respiratory drive, and respiratory muscle fatigue.

Stridor — Stridor occurs when there is airway obstruction. Inspiratory stridor suggests obstruction above the vocal cords (eg, foreign body, epiglottitis, angioedema). Expiratory stridor or mixed inspiratory and expiratory stridor suggests obstruction below the vocal cords (eg, croup, bacterial tracheitis, foreign body).

Angioedema – Angioedema can cause significant swelling of the lips, tongue, posterior pharynx, and most dangerously the larynx; this can occur over minutes to hours and may cause severe dyspnea. Etiologies include idiopathic, allergic (ie, anaphylaxis), medication-related (eg, nonsteroidal antiinflammatory drug [NSAID], angiotensin-converting enzyme [ACE] inhibitor, angiotensin receptor blocker), and complement-related (eg, C1-esterase inhibitor deficiency or a nonfunctional allele). Patients who receive IV tissue plasminogen activator (tPA) for acute ischemic stroke are also at risk for developing angioedema, which tends to be hemilingual and contralateral to the ischemic hemisphere [7].

Anaphylaxis – Anaphylaxis may cause severe swelling of the upper airway and tongue, and possibly airway occlusion. Bronchospasm may also be prominent. Symptoms and signs, which are often triggered by foods, insect bites, and various medications, develop over minutes to hours and may include skin and mucosal findings (eg, hives, flushing, oropharyngeal swelling), respiratory compromise (eg, wheezing, stridor, hypoxia), cardiovascular compromise (eg, hypotension, tachycardia, syncope), and gastrointestinal complaints (eg, abdominal pain, vomiting, and diarrhea).

Organophosphate poisoning – Acute toxicity from organophosphorus agents presents with manifestations of cholinergic excess (bradycardia, salivation, lacrimation, vomiting, diarrhea, bronchorrhea, miosis) and should be recognizable on rapid examination. Management typically involves endotracheal intubation and empiric antidotal therapy with atropine, pralidoxime, and benzodiazepines.

Pneumothorax – Any simple pneumothorax can develop into a life-threatening tension pneumothorax. Patients in extremis with a suggestive history and examination findings consistent with a tension pneumothorax (eg, hypotension, distended neck veins, unilateral diminished or absent breath sounds) should be treated with immediate needle decompression followed by a tube or catheter thoracostomy.

Methemoglobinemia – This abnormal hemoglobin variant can present with dyspnea, cyanosis, and an artifactual pulse oximetry reading of 85 to 88 percent that does not improve with supplemental oxygen. The diagnosis is confirmed by methemoglobin blood gas measurement (either arterial or venous) and treated with methylene blue.

Cardiac tamponade – Cardiac tamponade can be caused by trauma, malignancy, uremia, drugs, or infection and can present with acute dyspnea. The classic triad of hypotension, distended neck veins, and muffled heart tones suggest the diagnosis but are often absent.

Pulmonary embolism (PE) – The initial approach to patients with suspected massive PE should focus upon stabilizing the patient while clinical evaluation and definitive diagnostic testing are ongoing. Anticoagulation should be initiated even prior to confirming the diagnosis if risk-benefit regarding suspicion of PE and risk of bleeding appear favorable.

In patients who fail to improve with standard COPD treatment, re-evaluate for a PE, which may be responsible for up to 25 percent of apparent "COPD exacerbations."

Acute coronary syndrome (ACS) – Older adults and patients with diabetes who have a myocardial infarction may present with dyspnea as their sole symptom.

Cardiac arrhythmia – Cardiac rhythm abnormalities, such as atrial flutter, atrial fibrillation, and tachyarrhythmias (eg, supraventricular tachycardia [SVT] and ventricular tachycardia) can result in dyspnea. Such abnormalities may stem from underlying disease, including myocardial ischemia or cardiac decompensation due to the elevated heart rate or uncoordinated contractions.

The subjective feeling of dyspnea often improves with slowing down the rate of a tachycardic rhythm.

Fever – Fever can be associated with an infection, hypersensitivity pneumonitis, aspiration pneumonitis, PE, or poisoning (eg, aspirin overdose can cause hyperthermia and tachypnea).

Paroxysmal nocturnal dyspnea (PND) – Keep in mind that PND is not specific for ADHF. Patients with COPD may present with a similar history.

ough and sputum – Purulent sputum suggests bronchitis or pneumonia, and pink frothy sputum suggests ADHF. A nonproductive cough is a nonspecific symptom and may be associated with asthma, heart failure, respiratory infection, or PE.

Acute respiratory distress syndrome (ARDS) can occur following overdose of various drugs (eg, aspirin, cocaine, opioids, phenothiazines, and tricyclic antidepressants).

Psychogenic causes of acute dyspnea are diagnoses of exclusion in the ED; organic causes must be thoroughly considered first. Nevertheless, among patients younger than age 40 with no medical conditions, psychogenic dyspnea (eg, anxiety, panic attack) may be the cause in a sizable minority of patients [9,10].

Physical examination — Perform a more thorough physical examination after the initial rapid screen and any necessary stabilization is completed. Important signs are discussed below and in the accompanying table (table 4).

An unremarkable pulmonary and cardiac examination does not rule out significant disease. As examples, the sensitivity and specificity of the pulmonary examination are limited for making the diagnosis of pneumonia or ADHF [11-15].

Respiratory rate – Patients with serious underlying disease may have a fast, normal, or slow respiratory rate. As an example, patients with PE may have a respiratory rate in the normal range. Measurements of the respiratory rate obtained during triage may not be accurate [16,17].

Pulse oximetry – Pulse oximetry provides crucial information about arterial oxygenation and should be checked upon presentation to the ED in all patients complaining of dyspnea. Examining the waveform, if feasible, can help ensure accuracy since many conditions can cause erroneous readings (table 5). Standard pulse oximeters are not accurate in the setting of hypothermia, shock, carbon monoxide poisoning, and methemoglobinemia. Pulse oximetry may miss hypoxia, especially in patients with darkly pigmented skin [18].

In general, healthy individuals demonstrate an oxygen saturation (SpO₂) of 95 percent or greater. Older adults and patients with obesity or who smoke heavily often maintain saturation between 92 and 95 percent, while patients with severe chronic lung disease may have baseline saturation below 92 percent. In the setting of acute dyspnea, saturations that are lower than expected or lower than a patient's known baseline should be investigated and explained.

In a patient who complains of dyspnea on exertion, especially who is not hypoxic at rest, obtaining pulse oximetry while ambulating often provides useful data that can inform further testing and disposition. Worsening oxygen desaturation with ambulation can often change an anticipated discharge to an admission.

Jugular venous distension – Elevated jugular venous pressure may be present with ADHF, tension pneumothorax, cardiac tamponade, or any other cause of elevated intrathoracic pressure that prevents right heart filling. It can be assessed by observing the veins of the neck (movie 2) or examining hepatojugular reflux.

A number of conditions such as peritonitis, ruptured viscous, or bowel obstruction can cause severe pain that affects respiration and may manifest as acute shortness of breath, although this is generally not the patient's primary complaint [19]. (See "Evaluation of the adult with nontraumatic abdominal or flank pain in the emergency department".)

Ascites secondary to malignancy or liver disease can distend the abdominal cavity, placing pressure on the diaphragm and thereby increasing the work of breathing [20]. In such cases, dyspnea often improves after large-volume paracentesis. (See "Evaluation of adults with ascites".)

Obesity is a risk factor for obstructive sleep apnea and obesity hypoventilation syndrome, which can present with chronic dyspnea on exertion in addition to daytime hypersomnolence, hypoxemia, and hypercapnia. Additionally, increased abdominal pressure on the diaphragm can affect pulmonary function, and obesity has been associated with an increased risk of DVT and PE.

Supplemental oxygen can be started at 2 liters per minute (LPM) via nasal cannula with a target oxygen saturation of 94 to 98 percent.

COPD exacerbation – Do not withhold oxygen from patients with COPD, but lower the target saturation to 90 to 94 percent, with the understanding that this may reduce ventilatory drive and cause hypercarbia. However, failure to oxygenate the patient may have profoundly adverse consequences.

ACS – Excessive oxygen may be harmful in those with ACS. Administer oxygen for ACS only when the oxygen saturation is consistently below 94 percent.

An improvement in SpO₂ immediately after the administration of low-flow oxygen indicates a ventilation-perfusion (V/Q) mismatch.

Failure to improve with oxygen administration may indicate a right-to-left shunt or presence of methemoglobinemia.

In a patient with HIV (especially CD4 counts < 200 cells/microL) who presents with fever, cough, and dyspnea progressing over days to weeks, a profound drop in SpO₂ associated with ambulation is characteristic of Pneumocystis pneumonia.

Metabolic acidosis — Tachypnea and dyspnea can occur from respiratory compensation for metabolic acidosis, which is suggested by a low bicarbonate concentration (often defined as <23 mEq/L) on the serum chemistries. Evaluation includes confirmation with a blood gas and testing for specific causes (table 9).

A venous blood gas is generally sufficient (as compared with arterial blood gas) to confirm presence and assess degree of metabolic acidosis.

D-dimer – This test is not part of the workup of every patient with chest pain or shortness of breath and depends upon the patient's pretest probability for PE. Patients with a negative Pulmonary Embolism Rule-out Criteria (PERC) score (table 7) (calculator 1) can be ruled out for PE without D-dimer testing. Patients at low or moderate risk for PE according to a validated scoring system (eg, modified Wells criteria for PE) (table 8) and a negative enzyme-linked immunosorbent assay (ELISA) D-dimer can be ruled out for PE without further testing (algorithm 2 and algorithm 3).

BNP testing is not helpful when used indiscriminately in patients with acute, severe dyspnea, although it may be helpful in patients with a suspected cardiac origin [39].

• Less than 100 pg/mL – Negative predictive value of over 90 percent for ADHF.

• Between 100 pg/mL and 500 pg/mL – Cannot differentiate between ADHF and other causes of elevated BNP. Causes of a false-positive BNP (generally between 100 pg/mL and 500 pg/mL) include PE, fluid overload states (eg, renal failure, liver failure), critical illness, and other causes of right ventricular distension (eg, cor pulmonale, pulmonary hypertension).

• Greater than 500 pg/mL – Positive predictive value over 90 percent for ADHF.

Arterial blood gas – The role of arterial blood gas in the diagnosis and treatment of the acutely dyspneic patient is limited. The decision to perform tracheal intubation is based on clinical assessment and not on the arterial blood gas. Oxygenation is easily assessed using transcutaneous pulse oximetry. If there is any concern about pulse oximetry accuracy (table 5), we obtain an arterial blood gas. Acid-base status can be assessed using a venous blood gas and the serum bicarbonate. We do not routinely use arterial or venous blood gas for monitoring unless there is a discrepancy with pulse oximeter or capnography.

Chest MDCT – Even though chest MDCT will diagnose multiple problems, including malignancy, pneumonia, and pulmonary edema, it is most useful in dyspneic ED patients with trauma or concern for PE and when plain chest radiograph is inconclusive. MDCT does entail some risks, including contrast-induced nephropathy, allergic reaction to contrast, and radiation-related malignancy. MDCT should be performed when it is needed to establish an important diagnosis, even in patients with compromised kidney function since contrast-related kidney injury is relatively uncommon.

ADHF – Signs of ADHF that may appear on a CXR include cardiomegaly, cephalization of blood vessels, interstitial edema (eg, "Kerley B" lines, peribronchial cuffing), vascular congestion (image 1), and pleural effusions.

Radiographic findings can lag behind the clinical picture, and approximately 20 percent of patients admitted with ADHF have a nondiagnostic CXR [ 23].

ADHF is among the most common causes of acute respiratory failure among patients over 65 years of age.

Cardiomyopathy – The physiologic derangements associated with cardiomyopathy (primarily dilated cardiomyopathy) may result in pulmonary edema and manifest as dyspnea. CXR can appear similar to ADHF or just show cardiomegaly. Potential causes include cardiac ischemia, hypertension, alcohol abuse, cocaine abuse, and a number of systemic diseases (eg, sarcoidosis, systemic lupus erythematosus).

High-output heart failure – High-output heart failure may be precipitated by a number of conditions, including severe anemia, pregnancy, beriberi (thiamine deficiency), and thyrotoxicosis. Signs include tachycardia, bounding pulses, a venous hum heard over the internal jugular veins, and carotid bruits.

Pneumonia – Although an infiltrate on CXR is considered the "gold standard" for diagnosing pneumonia (image 2), radiographs obtained early in the clinical course may be nondiagnostic [26]. Volume depletion may also lead to a negative initial CXR. Contrary to past teaching, the appearance of the CXR (lobar versus diffuse disease) does not accurately predict the nature of the pneumonia (eg, "typical" versus "atypical" organisms).

Infection with COVID-19 can cause pneumonia. Common abnormal radiographic findings are consolidation and ground-glass opacities with bilateral, peripheral, and lower lung zone distributions. Lung involvement peaks in severity at 10 to 12 days after symptom onset.

Noncardiogenic pulmonary edema (ARDS) – ARDS can complicate a wide range of conditions and is characterized by rapidly progressive dyspnea, hypoxia, and bilateral infiltrates on CXR. It can be difficult to distinguish from ADHF purely on clinical grounds; BNP and echocardiography can be helpful in differentiation. Potential causes of ARDS include sepsis, shock, severe trauma, toxic inhalations (eg, aspiration, thermal injury, anhydrous ammonia, chlorine), infections (eg, COVID-19, hantavirus, severe acute respiratory syndrome [SARS], dengue, Middle East respiratory syndrome), blood transfusion, and drug overdose (eg, cocaine, opioids, aspirin).

High-altitude pulmonary edema (HAPE) – HAPE is a form of noncardiogenic pulmonary edema that typically occurs between two to four days after rapid ascent to elevations over 2500 meters (8000 feet). Symptoms often begin with a nonproductive cough, dyspnea on exertion, and fatigue and may progress quickly to dyspnea at rest. Pulmonary symptoms are often accompanied by a headache and occasionally cerebral edema.

Pneumothorax – A pneumothorax sufficient to cause acute dyspnea is usually visible on CXR (image 3 and image 4), while an additional expiratory view may be helpful [27]. In addition to trauma, vigorous coughing, and medical procedures (eg, central venous catheter placement, intubation, and barotrauma), a number of medical conditions (eg, COPD, cystic fibrosis, tuberculosis, Marfan syndrome, Pneumocystis pneumonia) increase the risk for developing a pneumothorax.

Pleural effusion, hemothorax – A moderate to large pleural effusion or hemothorax, which appear similar on CXR, can cause acute dyspnea. Common etiologies include infection, ascites, pancreatitis, cancer, heart failure, pneumonia, iatrogenic vessel transection, PE, and trauma. These are evaluated by cross-sectional imaging studies (eg, blood has high attenuation/Hounsfield units on CT) or by analysis of the pleural fluid.

Airway foreign body – Unilateral air trapping suggests a bronchial foreign body (image 6), but many organic foreign bodies are radiolucent and not evident on CXR [28]. Additionally, the absence of unilateral air trapping does not rule out a foreign body.

Acute chest syndrome – This potentially life-threatening complication of sickle cell disease typically has new pulmonary infiltrates on CXR. Patients generally complain of severe chest pain and acute dyspnea and have a fever. It is easily confused with pneumonia but should be considered in any patient with sickle cell disease.

EVALI – Initially described in 2019, EVALI is caused by e-cigarette use, especially among males younger than 35 years of age. It is primarily associated with vaping tetrahydrocannabinol (THC) products and strongly correlated with the presence of vitamin E acetate in the formulations [29,30]. EVALI is characterized by shortness of breath, cough, chest pain, and gastrointestinal complaints and diffuse hazy or consolidative opacities on CXR.

Lung cancer – Shortness of breath is a common symptom in patients with lung cancer at the time of diagnosis, occurring in approximately 25 percent of cases. Dyspnea may be due to extrinsic or intraluminal airway obstruction, obstructive pneumonitis or atelectasis, lymphangitic tumor spread, tumor emboli, pneumothorax, pleural effusion, or pericardial effusion with tamponade. (See "Clinical manifestations of lung cancer".)

CXR findings that should raise the suspicion for lung cancer include new lesions larger than 3 cm, measurable growth in any nodule or mass, pleural nodularity, and asymmetric or significantly enlarged hilar or paratracheal nodes. Concerning but less specific findings include pleural effusions and nondependent or substantial atelectasis.

Electrocardiogram — An ECG with ST segment changes is strong evidence for cardiac ischemia; however, the initial ECG is normal in approximately 20 percent of patients subsequently diagnosed with a myocardial infarction, and only 33 percent of initial ECGs are diagnostic.

The PERC rule has eight criteria (table 4) (calculator 3):

• Age <50 years

• Heart rate <100 beats/minute

• Oxyhemoglobin saturation ≥95 percent

• No hemoptysis

• No estrogen use

• No prior DVT or PE

• No unilateral leg swelling

• No surgery/trauma requiring hospitalization within the prior four weeks

In patients with a low probability of PE who fulfill all eight criteria, the likelihood of PE is sufficiently low that further testing is not indicated.

The modulation index, also known as the modulation factor, is a measure of the extent to which the amplitude of a carrier signal is varied in accordance with a modulating signal in a modulation system. Recalling the definition of the amplitude modulation \(s_{HF}(t) = (A + \gamma s(t)) \cos(\omega_{c}t)\), the modulation index is defined as: \(\displaystyle m = \frac{\max|\gamma s(t)|}{A} = \frac{\gamma\cdot\max|s(t)|}{A}\)

D-dimer levels rise with age such that using the traditional cutoff value of <500 ng/mL (fibrinogen equivalent units) results in reduced specificity of D-dimer testing in older patients (>50 years), a population in whom PE is common. Several studies report its use [2,63,99-104] with the most commonly used formula for age adjustment as:

Age (if over 50 years) x 10 = cutoff value in ng/mL (fibrinogen equivalent units)

Approximately 10 percent of patients present with the symptoms of an infarcted lung, usually due to smaller, more peripheral emboli. Pleuritic pain is typical in this population due to inflammation of the pleura. Hemorrhage from the infarcted lung is also thought to be responsible for hemoptysis.

To find the balances of all of your accounts, run this command:

$ ledger -f drewr3.dat balance

A more useful report is to show only your Assets and Liabilities:

$ ledger -f drewr3.dat balance Assets Liabilities

To show all transactions and a running total:

$ ledger -f drewr3.dat register

To limit transactions to a useful subset, simply add the accounts you are interested in seeing transactions for to the register command:

$ ledger -f drewr3.dat register Groceries

The final total of the register report for an account will match the balance of the same account, e.g.

Which matches the balance reported for the ‘ Groceries ’ account:

$ ledger -f drewr3.dat balance Groceries

If you would like to find transaction to only a certain payee use ‘ payee ’ or ‘ @ ’:

$ ledger -f drewr3.dat register payee "Organic"

There are three kinds of situations of modulation index of amplitude modulation:

- Undermodulation occurs when \(m < 100\%\).

- 100% modulation occurs when \(m = 100\%\).

- Overmodulation occurs when \(m > 100\%\), preventing envelope detection.

If however, you do have python installed but not pip , then the best instructions for what to do next are on the python website.

Based on \(\displaystyle s_{HF}(t)=A\cos(\omega_{c}t)+ \frac{\gamma}{2}\cos\left((\omega_{c}-\omega_{i})t\right)+ \frac{\gamma}{2}\cos\left((\omega_{c}+\omega_{i})t\right)\):
- Power of carrier, based on Parseval's theorem: \(\displaystyle P_{\text {carrier }}=2\left(\frac{A}{2}\right)^2=\frac{A^2}{2}\).
- Power in sidebands, based on Parseval's theorem: \(\displaystyle P_{\text {sidebands }}=4\left(\frac{\gamma}{4}\right)^2=\frac{\gamma^2}{4}\).