In the figure below, we show an amplitude-modulated square wave, which we wish to compare against the standard square wave
(a) Show that the complex Fourier coefficients of the standard square wave are
(b) Find the complex Fourier coefficients of the amplitude-modulated square wave
(c) Explain how your answer in (b) reduces to your answer in (a) as α →0
Please help with detailed steps
Homework Answers
Add Answer to:
In the figure below, we show an amplitude-modulated square wave,
which we wish to compare against...
EXAMPLE 4.2 Fourier series of a square wave Consider the square wave of Figure 4.4. This signal i...
in MATLAB plot the following
EXAMPLE 4.2 Fourier series of a square wave Consider the square wave of Figure 4.4. This signal is common in physical systems. For ex- ample, this signal appears in many electronic oscillators as an intermediate step in the gener ation of a sinusoid We now calculate the Fourier coefficients of the square wave. Because V, 0< t < To/2 x(t) = from (4.23), it follows that ToJTo2 To/2 - e ikast To/2 The values at...
A square wave of amplitude A and period T can be defined as -A, 5<t<0, with...
A square wave of amplitude A and period T can be defined as -A, 5<t<0, with f(t) = f(t + T), since the function is periodic. Compute the Fourier series for the function in the form f(t) = aneinwot, n=- where wo = 21/T and the coefficients an are the complex Fourier coefficients. Show all your work. Make a simple sketch of the signal and its series. The FIR filter is defined by the filter coefficients bk = [3,-1,2,1] Write...
Can you write hand solutions and matlab code please? Q3) There is a square wave with...
Can you write hand solutions and matlab code please?
Q3) There is a square wave with the period of T=21. The amplitude is 3 between 0 and it The amplitude is 0 between 1 and 2 T. 2 3 4 5 a) Find the Fourier series coefficients of this square wave. a = x()ật Il x(t)cos(kt)dt bx = ( x(t)sin(kt)dt b) Using Matlab, plot the truncated Fourier series; (1) For k 0 to 10 (II) For k 0 to 1000...
Reproduce Figures 9.2b and 9.2c on MATLAB, assuming that the square wave (Figure 9.2b) is a...
Reproduce Figures 9.2b and 9.2c on MATLAB, assuming that the
square wave (Figure 9.2b) is a periodic symmetric square wave of
normalized amplitude (A=1). Each student group should
decide the power spectral density level of the channel noise.
Compute the Fourier transform of the periodic square wave.
clear all
close all
%%%%
T=12*pi; %number of period
x=linspace(0,T);
t=x/pi
y0=square(x); %square wave signal
y0ft=fft(y0); %calculating Fourier Transformof signal
y0fts=fftshift(y0ft);
y0ftFinal=abs(y0ft);
AWGN= rand(size(x)); %Calculating whit noise
Att=(1/3);
nSig= Att*AWGN;
y=y0+nSig; %Square wave...
1. When a sound wave passes through air, and we hear it, the air pressure where we are varies with time. the excess pressure above (and below) atmospheric pressure in a sound wave is given by the...
1. When a sound wave passes through air, and we hear it, the air pressure where we are varies with time. the excess pressure above (and below) atmospheric pressure in a sound wave is given by the graph below: p(t) t in seconds -1 (a) Show that the fundamental (n ) is 15 times smaller in amplitude compared to the second harmonic (n-2). Hint: Expand p() in a Fourier series to show this. It would be interesting to note that...
Please, please, explain the process and step by step how to solve this problem, I want to get the...
please, please, explain the process and step by step how to
solve this problem, I want to get the logic and process:
>> Do not simplify the answer. I already saw other
answers and still do not get the process how to solve
it<<
1. In class we found that the Fourier series of a unit amplitude square wave of period 2 seconds was given by x(t) = Σ 그etjnitt HTT odd (a) Show that this series can be rewritten...
Use MATLAB to : ("j" is the imaginary number.) The term lo is the fundamental frequency...
Use MATLAB to :
("j" is the imaginary number.) The term lo is the fundamental frequency of the periodic signal, 2/T, where T is the period. Frequencies nlo, where n is an integer, are the harmonics. This infinite sum is an exact representation of the original function. If we use a finite sum, where n goes from -N to N, we will get an approximation "X-(t)". In this problem we will calculate and plot the Fourier series representation of a...
Can someone explain each part of this solution I don’t understand Example 1 square wave Derive...
Can someone explain each part of this solution I don’t
understand
Example 1 square wave Derive the Fourier series (FS) representation of a square wave of period T with duty cycle τ-AT, where 0< B<1. The square wave is symmetrically defined over one period by a Heaviside unit-step function, as in Eq. (28) It! <汁 (77) The ordinary unit-step could also be used, but the Heaviside is more natural here because the FS representation will pass through the 1/2 point...
please explain all, thanks! 4. (60 pts) A particle in an infinite square well of width...
please explain all, thanks!
4. (60 pts) A particle in an infinite square well of width L has an initial wave function (x,t = 0) = Ax(L - x)2, OSX SL a) Find y(x, t) fort > 0. You first have to normalize the wave function. Hint: this is best expressed an infinite series: show that the wave function coefficients are on = * 31% (12 – n?)(1-(-1)") → (n = 87315 (12 - nºre?); n odd. b) Which energy...
Part I: Black Box A Design your first black box adhering to the following specifications A. Input Signal to Black Box A 1. A 1 kHz cosine wave with amplitude of 1V. B. Output Signal from Black Box A...
Part I: Black Box A Design your first black box adhering to the following specifications A. Input Signal to Black Box A 1. A 1 kHz cosine wave with amplitude of 1V. B. Output Signal from Black Box A 1. A 1 kHz sine wave with amplitude of Hint: Use an ideal op-amp C. Explain your design process. What type of circuit did you design? Discuss D. Why did vou use an op-amp? Could another component be used instead? Why...
in MATLAB plot the following
EXAMPLE 4.2 Fourier series of a square wave Consider the square wave of Figure 4.4. This signal is common in physical systems. For ex- ample, this signal appears in many electronic oscillators as an intermediate step in the gener ation of a sinusoid We now calculate the Fourier coefficients of the square wave. Because V, 0< t < To/2 x(t) = from (4.23), it follows that ToJTo2 To/2 - e ikast To/2 The values at...
A square wave of amplitude A and period T can be defined as -A, 5<t<0, with f(t) = f(t + T), since the function is periodic. Compute the Fourier series for the function in the form f(t) = aneinwot, n=- where wo = 21/T and the coefficients an are the complex Fourier coefficients. Show all your work. Make a simple sketch of the signal and its series. The FIR filter is defined by the filter coefficients bk = [3,-1,2,1] Write...
Can you write hand solutions and matlab code please?
Q3) There is a square wave with the period of T=21. The amplitude is 3 between 0 and it The amplitude is 0 between 1 and 2 T. 2 3 4 5 a) Find the Fourier series coefficients of this square wave. a = x()ật Il x(t)cos(kt)dt bx = ( x(t)sin(kt)dt b) Using Matlab, plot the truncated Fourier series; (1) For k 0 to 10 (II) For k 0 to 1000...
Reproduce Figures 9.2b and 9.2c on MATLAB, assuming that the
square wave (Figure 9.2b) is a periodic symmetric square wave of
normalized amplitude (A=1). Each student group should
decide the power spectral density level of the channel noise.
Compute the Fourier transform of the periodic square wave.
clear all
close all
%%%%
T=12*pi; %number of period
x=linspace(0,T);
t=x/pi
y0=square(x); %square wave signal
y0ft=fft(y0); %calculating Fourier Transformof signal
y0fts=fftshift(y0ft);
y0ftFinal=abs(y0ft);
AWGN= rand(size(x)); %Calculating whit noise
Att=(1/3);
nSig= Att*AWGN;
y=y0+nSig; %Square wave...
1. When a sound wave passes through air, and we hear it, the air pressure where we are varies with time. the excess pressure above (and below) atmospheric pressure in a sound wave is given by the graph below: p(t) t in seconds -1 (a) Show that the fundamental (n ) is 15 times smaller in amplitude compared to the second harmonic (n-2). Hint: Expand p() in a Fourier series to show this. It would be interesting to note that...
please, please, explain the process and step by step how to
solve this problem, I want to get the logic and process:
>> Do not simplify the answer. I already saw other
answers and still do not get the process how to solve
it<<
1. In class we found that the Fourier series of a unit amplitude square wave of period 2 seconds was given by x(t) = Σ 그etjnitt HTT odd (a) Show that this series can be rewritten...
Use MATLAB to :
("j" is the imaginary number.) The term lo is the fundamental frequency of the periodic signal, 2/T, where T is the period. Frequencies nlo, where n is an integer, are the harmonics. This infinite sum is an exact representation of the original function. If we use a finite sum, where n goes from -N to N, we will get an approximation "X-(t)". In this problem we will calculate and plot the Fourier series representation of a...
Can someone explain each part of this solution I don’t
understand
Example 1 square wave Derive the Fourier series (FS) representation of a square wave of period T with duty cycle τ-AT, where 0< B<1. The square wave is symmetrically defined over one period by a Heaviside unit-step function, as in Eq. (28) It! <汁 (77) The ordinary unit-step could also be used, but the Heaviside is more natural here because the FS representation will pass through the 1/2 point...
please explain all, thanks!
4. (60 pts) A particle in an infinite square well of width L has an initial wave function (x,t = 0) = Ax(L - x)2, OSX SL a) Find y(x, t) fort > 0. You first have to normalize the wave function. Hint: this is best expressed an infinite series: show that the wave function coefficients are on = * 31% (12 – n?)(1-(-1)") → (n = 87315 (12 - nºre?); n odd. b) Which energy...
Part I: Black Box A Design your first black box adhering to the following specifications A. Input Signal to Black Box A 1. A 1 kHz cosine wave with amplitude of 1V. B. Output Signal from Black Box A 1. A 1 kHz sine wave with amplitude of Hint: Use an ideal op-amp C. Explain your design process. What type of circuit did you design? Discuss D. Why did vou use an op-amp? Could another component be used instead? Why...
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