An alternative to using a Gaussian function for h(t) in the computation of the STFT, it is K cos² (πt/T) -T/2≤t≤T/2 0 otherwise proposed to use the function h(t) =< K>0 is adjusted for unit energy. One advantage of this function over the Gaussina function is that it is of finite (rather than infinite) duration. a) Show that in order to make h(t) have unit energy, K must be set to the value K = √√8/(37). As with other problems, this result cannot be reverse engineered. b) Using the modified definition of the Fourier Transform and taking advantage of symmetries in the function given, show 4T sinc(@T/2π) c) 3π (2π)²-(WT)² Let x(t) be the signal x(t)= e defined -∞0 and

An alternative to using a Gaussian function for h(t) in the computation of the STFT, it is K cos² (πt/T) -T/2≤t≤T/2 0 otherwise proposed to use the function h(t) =< K>0 is adjusted for unit energy. One advantage of this function over the Gaussina function is that it is of finite (rather than infinite) duration. a) Show that in order to make h(t) have unit energy, K must be set to the value K = √√8/(37). As with other problems, this result cannot be reverse engineered. b) Using the modified definition of the Fourier Transform and taking advantage of symmetries in the function given, show 4T sinc(@T/2π) c) 3π (2π)²-(WT)² Let x(t) be the signal x(t)= e defined -∞0 and

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

In Electrical Engineering, the periodic especially sinusoidal signals arise frequently. A periodic function p(t) with the fundamental period T, satisfies p(t)=p(t+kT) for all t and all integer k. We define a sinusoidal signal as z(t)=Z,+ZpeakCOS(ot+¢), where Z, is the offset, Zpeak is the peak value, w=27 /T=2tf is the angular frequency (in rad/s), o is the phase (in radians), T is the period and f is the frequency (in Hz=s'). Note that, these are Ao, C1, 0 and T in the figure below. (Note: The phase ø is defined in radians. However, we often write it in degrees!) 2.5 1.5 1 Ao T 0.5 -1 1 2 3 t[s] a. Express a sine wave (i.e. y(t)=YpeakSin(wt)) in the form given above. реа b. Let us given the signal r(t)=-5+10cos(314t-45°). Find the offset, peak, frequency, period and phase of this signal. c. The rms (root-mean-square) value Pms (also, nominal value or effective value) of a periodic function p(t) is defined as P dt . Note that, the %3D integration should be on a full-period and the…
A step voltage is applied to a series C−R circuit. When the capacitor is fully charged the circuit is suddenly broken. Deduce, using Laplace transforms, an expression for the capacitor voltage during the transient period if the voltage when the supply is cut is V volts.
4. For the system shown in Figure P7.3, what steady- state error can be expected for the following test inputs: 15u(t), 15tu(1), 15u(t). [Section: 7.2] R(s) S+3 3 45 FIGURE P7.3
The circuit has a switch that closes at t=0. Resistor R = 2.6ohms. L=0.1H, C= 4F while Vs= 24 volts
Consider the circuit shown below, where VA = 4 u(t). Vg-6 u(t) and C-1 F. nitially there is no energy stored in the circuit. VA Ve Find the value of voſt), when E 25. (Hint First determine the expression for vot), then evaluate in for t=25 by replacing t term with 2) In your answer, use only one digit after the decimal point and do NOT include the unit. (For exarmple, if you find the output voltage at t=2s as 3.456 V, write 3.5) Use point (.) as the decimal point. Do not use comma (.). A Click Submit to complete this assessment. «E Question 2 o
Answer All questions: QI: Connect the block diagram shown below. If A=1, trace on the oscilloscope the step function, Vol and Vo2. What is the steady state error? Verify that the function et and are L.T pairs. +1 Vo?
Problem 1.3 (Sinusoids and Exponentials) All signals are defined for -o < t < 00 (a) Sketch the sinusoid xa(t) = 2 cos(10rt + t/6). What is its fundamental period? (b) Repeat part (a) but for the sinusoid xb(t) = 5 sin(19rt – n/3). (c) What is the fundamental period of x.(t) = Xa(t) + xb(t)? HINT: It is not the fundamental period of Xa(t) nor xá(t). (d) Sketch the exponential xa(t) = e-l/5, What is its time constant? (e) Sketch the signal xe(t) = Xa(t)Xa(t). -
Please give a clear, detailed, step-by-step explaination. I'm just as interested in the correct process of how to approach this problem as I am in the correct answer. Thank you in advance!
cos(4(pi) - j(pi)) is equivalent to: a.) -7.58-j7.84 b.) 7.58+j8.75 c.) -7.58-j8.74 d.) -7.58+j7.84
The discrete time system is described by, y(n) = x(n) + nx(n-1). Check whether this system is causal/time variant.
Give a correct answer and be sure to include the proper unit of time..