Q5. A Hann (sometimes called a cosine bell) window function h(t/T) can be defined1+ cos )|| < {h(t/T) =(a) Sketch this window function.(b) Is this function odd or even? What are the consequences for its Fourier transform?(c) Determine the Fourier transform of this window function h(t/T).(d) Determine the width of the largest peak in the Fourier transform of the window functionh(t/T) using the values of the first zero crossings.(e) Hence, compare the width of the the largest peak in the spectrum with the equivalentmeasure for a flat-top, rectangular window function of the same temporal width,rect(t/T).(f) Describe how the perceived spectrum of a periodic signal is modified due to a givenwindow function.(g) If the time-window T on a spectrum analyser consists of 256 discrete samples, what isthe maximum frequency vmax which can be measured whilst avoiding aliasing issues?

"According to the Company's policy, we will provide solution of first three sub-parts of the given…

Q5. A Hann (sometimes called a cosine bell) window function h(t/T) can be defined (1+ cos ) |4| < { h(t/T) = (a) Sketch this window function. (b) Is this function odd or even? What are the consequences for its Fourier transform? (c) Determine the Fourier transform of this window function h(t/T).

Q5. A Hann (sometimes called a cosine bell) window function h(t/T) can be defined (1+ cos ) |4| < { h(t/T) = (a) Sketch this window function. (b) Is this function odd or even? What are the consequences for its Fourier transform? (c) Determine the Fourier transform of this window function h(t/T).

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

Related questions

Q: Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t- a)] = e -j2rva TF [f (t)] where aER…

Q: Q4) Fourier transformation a) What are the spatial and frequency ranges? b) How can you transform a…

Q: Consider the following signal: cos(20Tt) te [-1,1] x(t) te [-2, –1) u (1, 2] 6. Assuming the signal…

Q: For given periodic signal g(t), what can be inferred about Fourier series coefficients (FSC)? In…

A: The time domain signals can be continuous or discrete. The time domain signals can be periodic as…

Q: An odd function decomposed in Fourier series has cosine components ? True OR False

A: fourier series is the representation of function in terms of sine and cosine hormonics which are…

Q: Q5: Write a representation of f (t) shown below as a complex exponential fourier series. Over…

A: Solution a

Q: An FM singla has an intelligence frequency of 5 kHz and a maximum deviation of 20 kHz. How many…

A: Modulation is a technique of superimposing the message signal into a carrier signal. In the…

Q: 3.5. Let x1(t) be a continuous-time periodic signal with fundamental frequency wj and Fourier…

Q: The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as Cx =…

Q: Compute discrete time Fourier Series coefficients and obtain discrete time Fourier series…

A: Given n=5 x1[n]=cosπ4n x[n]=∑k=-∞k=∞ x1[n-4k]u[n-4k]-u[n-4k-4]

Q: Imagine a plane wave ofamplitude Eoimpinging normally on a large horizontal ruling, which is a…

Q: Question 3-) Consider two discrete signals x1[k] and x2[k]. Let æ1[k], x2[k] be periodic nals with…

Q: Which of the following is considered an efficient algorithm for finding the discrete Fourier…

A: To find the efficient method

Q: Given the fourier transform of is , what is the Fourier transform of ?

A: According to the question,

Q: Type using Kepord or will dislike can anyone explain what the discussion could be make from the…

A: Fourier transform provides a frequency domain description of time domain signals. It is an extension…

Q: 1)For the discrete-time signal given as x [n] = [4,5,2,1,5,6,2,1], the Fast Fourier coefficients are…

Q: Representing a signal (image) in a Fourier series representation with a complex exponential…

A: We need to write the given trigonometric Fourier series into complex Fourier series and draw…

Q: A discrete-time signal z[n] has a period of N > 2. Which of the following is/are always true about…

A: According to the properties CK=CN+K=CN-K ||CK+a||=||CN-K-a||=||CN+K+a||. where a is a constant /_ Ck…

Q: In signal Processing, what is the purpose of Fourier Series on ECG Signals? Cite at least 3

A: Purpose of Fourier series on ECG signals : It is known that Fourier series is only applicable for…

Q: QUESTION 3 a. Consider the aperiodic signal of Figure Q3(a), xı(t). What is its Fourier Transform,…

A: X1(ω) = ∫-∞∞x(t)e-jωt dt = ∫-2-1 A e-jωt dt +∫21 A e-jωt dt=A e-jωt-jωt=-2t=-1+A e-jωt-jω21…

Q: Obtain the Fourier transform of a rectangular function. Also sketch its magnitude spectrum.

A: i have explained in detail

Q: Problem 4 Consider a continuous-time LTI system whose frequency response H(jw) is shown graphically…

A: a)

Q: (A) A rectangular pulse x(t) of width t= 8 msec. and amplitude A=10 V is centered at the origin in…

A: As per our company guidelines we are supposed to answer only first 3 subpart kindly repost other…

Q: 1. What does the Fourier series analysis tells us about digital signal? Explain your answer

A: We are authorized to answer 1 question at a time so i am answering only 1 please resubmit the…

Q: Consider the periodic signal x(t) given by the expression x(t) = (2 + 2j)e-j3t – 3je¬j2t + 5+ 3je]2t…

A: NOTE: Since you have posted a question with multiple subparts, we will solve the first three…

Q: A. Consider the two signals whose Fourier Series Spectrum as shown below. Assume that the units of…

A: Answer(A) When two signals are multiplied in the frequency domain The Fourier series spectrum of…

Q: A Fourier series is given as: f(t) = 2 + 2 cos 3t – 3 sin 3t + cos 5t + sin 5t – 0.5 cos 6t + 0.2…

A: According to the question we have to calculate fundamental frequency, find the Fourier series in a…

Q: Find the Fourier coefficients c0, c1, c2, c3 for the discrete time signal given as x [n] =…

Q: [Part C-C3 (A) A rectangular pulse x(t) of width t= 8 msec. and amplitude A=10 V is centered at the…

A: Given : Amplitude of the signal A = 10 V Width of the signal T = 8 m Sec. Here first of all…

Q: (1) Compute the signal power and signal energy for the discrete-time signal x(n ) = e10jn u(n) .…

A: Solution(1)- (1) Given,x[n]=e10jnu[n]so,x[n]=e10jnu[n]The signal energy,E=∑nx[n]2 E=∑n=0∞…

Q: Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t - a)] = e-2nva TE (f (t)] where aeR *.…

A: Given: h(t)=0, -∞<t<0t2-t+0.25, 0≤t<10, 1≤t<∞ i) We need to plot h(t) ii) We need to…

Q: Answer the following four questions according to the following signal below: 1)the frequency of the…

A: We are authorized to answer only 3 subparts at a time since you have not mentioned which part you…

Q: Show that the trigonometric fourier series of a periodic signal f(t) containing fourier coefficient…

Q: Q3) For the discrete-time signal, x[n] = )" Where In| is the absolute value of n, (a) Find the…

A: The time domain signals can be continuous or discrete. The time domain signals can be periodic as…

Q: If a signal's frequency spectrum has only discrete components ranging from 0 to infinite. What the…

A: Discrete components which are containing a single component or may be two components in some cases…

Q: Suppose we are given the following information about a signal x[n]: 1. x[n] is a real and even…

Q: Q2. (a) Determine the Fourier transform of a Hann (sometimes called a raised cosine) window function…

A: Given : h(t) = 121+cos2πtT t<T20 t≥T2h(t) =121+cos 2πtT…

Q: Take the periodic input with period 4, and values in the range of indices 0, to 3 given as х 3D {1,…

A: "According to the Company's policy we will provide solution of the first part the question as to the…

Q: Question (3):. (i) (ii) Which is the fourier transform of the given time signal? -T Alternative I)…

Q: Signal & Systems Describe by using your own word when the Fourier Series representation is used and…

A: We need to tell about Fourier series coefficient .

Q: Explain with an example, the compromise between frequency resolution and time resolution in the…

A: Bartlett Method- Bartlett method is used for the estimation of power spectra. It gives a way to…

Q: C) Put (TRUE) or (FALSE) and say why : Fourier series is only applicable for periodic signals.

A: Fourier series concept is aonly applicable for periodic signal whereas fourier trasform is…

Q: a. Which of the following is true? The Fourier transform of a unit rectangular pulse is A.…

A: NOTE :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Consider the following continuous time system that sums two input signal z1(t) and z2(t) with aj and…

A: Any continuous time periodic signals can be represented as an infinite sum of sine and cosine…

Q: . For a signal x(n)=[2,4,6,8,10,12,14,16] defined for n=0to7, evaluate the Fast Fourier Transform…

A: given signal xn=2,4,6,8,10,12,14,16for n=0 to 7

Q: A function y=Rx) is defined by Domain ,: xe (,+){±2,±6,±10,±14,..} (3 if - 2< x<0 S(x)=? 3-x if 0<x…

Q: The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as…

A: Given: A discrete-time signal xn=2,1,-4,2 with period N = 4 has Fourier coefficients as…

Concept explainers

Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental frequency and harmonics) through a process called Fourier analysis.

Question

Q5. A Hann (sometimes called a cosine bell) window function h(t/T) can be defined
1+ cos )
|| < {
h(t/T) =
(a) Sketch this window function.
(b) Is this function odd or even? What are the consequences for its Fourier transform?
(c) Determine the Fourier transform of this window function h(t/T).
(d) Determine the width of the largest peak in the Fourier transform of the window function
h(t/T) using the values of the first zero crossings.
(e) Hence, compare the width of the the largest peak in the spectrum with the equivalent
measure for a flat-top, rectangular window function of the same temporal width,
rect(t/T).
(f) Describe how the perceived spectrum of a periodic signal is modified due to a given
window function.
(g) If the time-window T on a spectrum analyser consists of 256 discrete samples, what is
the maximum frequency vmax which can be measured whilst avoiding aliasing issues?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

a. Show that 2-D discrete Fourier Transform of a M × N digital image is periodic.That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center ofthe 2-D array of frequency plane.
a) Make a plot of the normalized fft magnitude as a function of frequency (real frequency in Hz). Only display the frequency range between -1kHz and 1kHz. b) On the same figure as part (c), superimpose the magnitude of the Fourier series coefficients, |??|, as a function of frequency as a stem plot. Again, only display the frequency range between -1kHz and 1kHz. How well do they compare? Hint*: Consider making a frequency vector containing only the Fourier harmonic frequencie
how to solve fourier series question and concepts ?
The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as ck=(c-8,c-7,c-6,6-j,c-4,c-3,-5,c-1,c0,c1,-5,6-j) .Find the missing coefficients and plot its magnitude spectrum for -8≤k≤3.
Consider the following discrete time signal periodic with N?[?]=1+sin(2??)?+3cos(2??)?+cos(4???+?2)Find the Fourier series representation of ?[?], i.e. find the Fourier series coefficients ?0, ?−1, ?1, ?−2 and ?2.
What does the Fourier series analysis tells us about digital signal? Explain your answer.
Consider the periodic signal ?(?) given by the expression x(t) = (2 + 2j)[e^(−j3t)] – 3j[e^(−j2t)] + 5 +3j(e^(j2t) + (2 – 2j)e^(j3t) . a) What is the fundamental frequency of x(t)? b) Find and plot the magnitude and phase of the Fourier series coefficients as a function of frequency. c) Is x(t) a real signal? Why? d) Compute the total power of x(t) using Parseval’s relation.
What are some cool/interesting applications of Fourier Series or Fourier Analysis that are not mentioned a lot?
Obtain the Fourier Transform to the rectangular pulse of duration 2 second and having a magnitude of 10 volts.
Find the Continuous-Time Fourier Series coefficients for the following continuous-time signal: ?(?) = ? 0 < ? < 4 with a fundamental period of ? = 4
An FM singla has an intelligence frequency of 5 kHz and a maximum deviation of 20 kHz. How many sidebands are produced with significant amplitudes? Use the Bessel Table.
Derive the compact trigonometric Fourier series for the waveform