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Question 1: Continuous Signal Analysis Question: Consider a continuous-time signal
x(t)=2cos(2πf
1
t)+3sin(2πf
2t), where1=5f
​=5 Hz and2=10f2
=10 Hz. Calculate the signal's frequency components.
Answer: The signal
x(t) contains two frequency components,
F 1 and2f2, at amplitudes 2 and 3, respectively.
Question 2: Continuous Fourier Transform Question: Find the Fourier Transform of the continuous-time
signal
x(t)=e
−atu(t), where
u(t) is the unit step function.
Answer: The Fourier Transform of
x(t) isX(f)=a+j2πf1
, where
j represents the imaginary unit.
Question 3: Sampling Theorem Question: What is the Nyquist rate for a continuous signal with a maximum
frequency component of 1000 Hz?
Answer: The Nyquist rate is twice the maximum frequency component. So, in this case, it would be
2×1000
2×1000 Hz, which is 2000 Hz.
Question 4: Discrete Signal Convolution Question: Given two discrete signals
x[n]={1,2,1} and
ℎ={1,−1,2}
h[n]={1,−1,2}, find the convolution
y[n]=x[n]∗h[n].
Answer: The convolution
y[n] is
{1,1,3,3,4,2}
{1,1,3,3,4,2}.
Question 6: Discrete Fourier Transform (DFT) Question: Compute the 4-point DFT of the sequence
x[n]={1,1,1,1}.
Answer: The DFT of
x[n] is
{4,0,0,0}
{4,0,0,0}.
Question 7: Convolution Theorem Question: Using the convolution theorem, find the convolution of
h[n]={1,−1,2}.
Answer: By taking the Fourier Transform of
x[n] and
h[n], multiplying them in the frequency domain, and then applying the inverse Fourier Transform, you would get
Thank you

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🚀 Need Expert MATLAB Assignment Help? Look No Further! 📊

  • 1.
  • 2. Question 1: Continuous Signal Analysis Question: Consider a continuous-time signal x(t)=2cos(2πf 1 t)+3sin(2πf 2t), where1=5f ​=5 Hz and2=10f2 =10 Hz. Calculate the signal's frequency components. Answer: The signal x(t) contains two frequency components, F 1 and2f2, at amplitudes 2 and 3, respectively.
  • 3. Question 2: Continuous Fourier Transform Question: Find the Fourier Transform of the continuous-time signal x(t)=e −atu(t), where u(t) is the unit step function. Answer: The Fourier Transform of x(t) isX(f)=a+j2πf1 , where j represents the imaginary unit.
  • 4. Question 3: Sampling Theorem Question: What is the Nyquist rate for a continuous signal with a maximum frequency component of 1000 Hz? Answer: The Nyquist rate is twice the maximum frequency component. So, in this case, it would be 2×1000 2×1000 Hz, which is 2000 Hz. Question 4: Discrete Signal Convolution Question: Given two discrete signals x[n]={1,2,1} and ℎ={1,−1,2} h[n]={1,−1,2}, find the convolution y[n]=x[n]∗h[n]. Answer: The convolution y[n] is {1,1,3,3,4,2} {1,1,3,3,4,2}.
  • 5. Question 6: Discrete Fourier Transform (DFT) Question: Compute the 4-point DFT of the sequence x[n]={1,1,1,1}. Answer: The DFT of x[n] is {4,0,0,0} {4,0,0,0}. Question 7: Convolution Theorem Question: Using the convolution theorem, find the convolution of h[n]={1,−1,2}. Answer: By taking the Fourier Transform of x[n] and h[n], multiplying them in the frequency domain, and then applying the inverse Fourier Transform, you would get