# Questions tagged [homework]

Homework means the asker is requesting help with school homework. This lets potential answerers know that they should guide the student in solving the problem, rather than simply showing the complete answer.

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### How to Implement the moving average filter in time domain in MATLAB? [closed]

I have a sinusoidal x(t) = sin(500πt) signal is corrupted by random noise. The corrupted signal is sampled with sampling frequency fs = 5 kHz and passed through a 5-point moving average filter to ...
50 views

### Calculate the power of a discrete-time signal

We got this question in our test :- $$S(t) = 5\cos(10πt - π/2) + 6\sin(15πt)\cos(15πt)$$ My Solution :- $$S(t) = 5\cos(10πt - π/2) + 3\sin(30πt)\qquad \textrm{[Using \sin(2A) = 2\sin(A)\cos(A)]}$$...
277 views

### Finding the impulse response given response to another signal

I was trying to solve this question : I respresented $x(t) = u(t+1)-u(t-1)$ writing the convolution as $[u(t+1)-u(t-1)]*h(t) = y(t)$ I then used the property of differentiation to convert from the ...
1 vote
87 views

### Impulse Response of real coefficient, LTI System

I'm trying to obtain the impulse response $h[n]$ of a system whose frequency response is $H(e^{j\omega})=R(\omega)e^{-25j\omega}$. I believed that $h[n]=h[n-25]$, would be the correct answer, however ...
81 views

### Stft of sinusoids

I have a sinusoidal signal of 10 minutes. For the first 5 minutes, the signal has a frequency of 100 Hz and for the next 5 minutes, the signal has a frequency of 200 Hz. 1 - If I look at the ...
1 vote
3k views

### Minimum sampling frequency, quantization, and bitrate calculation

An analogue sensor has a bandwidth which extends from very low frequencies up to a maximum of 14.5 kHz. Using the Sampling Theorem what is the minimum sampling rate (number of samples per second) ...
38 views

### DTFT Pairs confusion

When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is ...
1k views

410 views

### How can I find expansion coefficients of the a vector in a given basis?

How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors? Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$ What are the expansion ...
142 views

### How to find average and power of a signal

I need to find the average and the power of this signal: $$x(n)=\sum_{k=1}^{\infty}2^{-k}e^{j2{\pi}kn}$$ The problem is that the summation starts at 1 and not at 0, and a part of that how can I find ...
1 vote
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538 views

### Compute output given input, transfer function and initial conditions

The problem statement is Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
1 vote
404 views

### Deriving of magnitude, phase response and impulse response of transfer function

I have a transfer function as $$H(z) = \frac{-0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z - 0.0625}{z^4}$$ I want to derive magnitude and phase response of this equation. can someone help me from here I ...
1 vote
67 views

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### impulse response cascaded with time reversed of itself

Consider a filter with real-valued impulse response $h[n]$. The filter is cascaded with another filter whose impulse response is $h'[n] = h[-n]$, i.e. whose impulse response is the time-reversed ...
1 vote
436 views

### Determining time-invariance of a system

I have a question about determining time-invariance of a linear system. We are given this system and we need to determine if it is time-invariant or not: $$y(t)=\int_{-t}^{\infty}x(-3\tau)d\tau$$ ...
1 vote
911 views

### Determine the Z-Transform for the following sequence: $|n|(\frac{1}{2})^{|n|}$

Determine the Z-Transform for the following sequence: $$|n|(\frac{1}{2})^{|n|}$$ I have tried to solve the above problem. However, the answer that I got is the negative of what is given in the ...
93 views

### Finding inverse Z Transform

Find the inverse Z transform: I have done the solution but my answer does not match with the one given in the textbook. What I may have done wrong?
650 views

### How to determine whether a filter is high/low or band pass from the Z transform?

How to solve questions of these kind? I have tried by replacing $z=re^{jw}$ and taking the limits from $0$ to $\infty$. But I am not sure what $e^{j\infty}$ is.
1 vote
148 views

### Invertibility of an ideal differentiator

Is the system $y(t)= dx(t)/dt$ invertible or not? If yes, please determine the inverse system for it.
1k views

### Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $H(\omega)$. I don't have any clue that how to deal with the ...
70 views

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### Calculating the magnitude spectrum and phase spectrum

From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$. Then, I want to calculate its magnitude spectrum and phase spectrum. The ...
1 vote
2k views

### How to match zero-pole diagrams to their frequency responses (Discrete Time)

I get confused when there are a lot of zeros/poles in the zero-pole diagram and I find difficulty understanding their frequency response. I know the following: 1. Complex conjugates cause double ...
1 vote
376 views

### Adaptive equalization vs inverse of transfer function

I have the following equalization problem as shown in the figure below: Now I can compute the coefficients for my adaptive FIR filter c (dim(c) = N) the following: \$\mathbf{c_{opt}} = (\mathbf{H}^T\...
249 views

### Discrete Fourier Transform in Signal Processing - Interpreting graphs of transformed signals

Given above are the real parts of the signals I to IV. Which of the following statements are correct? (i): Signal III is the result of the discrete Fourier transform of signal I. The associated ...
142 views

### Change phase of the output of a buffer

I have a question about changing the phase of a buffer. Question - How to change the output phase of a buffer by 90 degrees, 180 degrees, and 270 degrees? I know to change the phase by 180 degrees, ...
1 vote
34 views

### Explain if the following processes are stable or not

I have got a question about my homework and was wondering if anybody could help. In the picture below you can see the processes. I need to determine whether they are stable or not. Now I have only ...
I have a discrete signal that goes as follows: $$x[n]=[-1,4,-1,0]$$ I have already done the DFT for the signal, with the following result: $$X = 2, X=-4i,X=-6,X=4i$$ But for some reason, I ...