Signals & Systems by Mahmood Nahvi

By Mahmood Nahvi

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The fine structure of (b) is revealed in (c) and (d). 1 An energy signal A signal picked up by a microwave antenna is modeled by the sinusoidal function v(t) = A cos(ωt + θ ), where ω = 2π f and f = 100 MHz. The signal lasts only T seconds. Find the total energy in the signal as a function of A and T , and compute its value when A = 1 mV and T = 1 µsec. 5 pJ. 2 Dual-tone multi-frequency signaling (DTMF) Touch-tone telephones dial using DTMF signaling. In this DTMF system each decimal digit (0 to 9) is identified by a signal that is the sum of two pure tones, one from lowband and another from high-band frequencies.

Edu/kw/ecg/. 11 (a) Twelve consecutive cycles of continuous EKG recording (lead V5 recorded by the electrode on the left side of the chest). Each division on the chart paper is 1 mm. One division on the time axis is 40 msec (a total of about 3 seconds and 4 beats on the lower trace), resulting in a rate of about 70 beats per minute (BPM). In practice, the BPM number is read directly off the chart (see text). 5 mV. Note the remarkable reproduction of the waveform in each cycle. 11(b). 11 (b) Schematic representation of one cycle of an EKG and its noted components, recognized and understood as the manifestations of the physiological activity of the heart: P-wave (depolarization of the atria) QRS complex (depolarization of the ventricular muscle) ST-T wave (repolarization of the ventricular muscle) recordings between each two electrodes, with the third electrode acting as the reference ground.

26). direction of increasing t), the slope of the tangent to the exponential is 1 A/s. Therefore, for small values of t such as t < 5 ms, the exponential can be approximated by its tangent line i = 1 − t/1,000 A. 9950125 A. 001% (or one in 100,000) % = 100 × This is an extremely small error, prompting an approximation of capacitor current by the flat line of a unit-step function. ) 44 CHAPTER 1 Introduction to Signals b. The unit impulse is derivative of unit step. The responses of the circuit to the unit-impulse voltage are derivatives of its responses to unit-step voltage.

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