# 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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### Axes of Discrete Fourier Transform

Problem Given $X[k] = \sum_{n=0}^{N-1} x[n]e^{-j2\pi kn/N}, k = 0, ..., N-1$ What are the units on the x-axis and y-axis? Note that for the x-axis there are two answers. Attempted solution My first ...
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### Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab

I have been given an input and output signal. input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1) output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n). or x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
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### How would one solve this question if no initial conditions are given? Which assumption can I make?

This was a question on our test, I know it can be easily solved by Z-transforms but there are no initial conditions specified. In this case, what would be the right approach? Assume all initial ...
1 vote
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### How to do appcoef and detcoef using pyWavelets?

I am new to signal processing and currently doing a school project in wavelet transform using Python. I want to extract all details and approximations (Example: cA2, cA1, cD2, cD1), pywt could return ...
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### Multilevel DWT wavedec - How to get each coefficient (approximations and details) in the same length as the original signal?

I am doing a school project referring to the research paper https://www.tandfonline.com/doi/abs/10.1080/0952813X.2013.813976?journalCode=teta20 The overall concept of the research is as the following ...
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### How to design a Controller that would adjust the steady-state error of a system?

I have a simple model (input-plant-output) with a transfer function : $$T(s)=\frac{4}{s^{2}+2s+4}$$ The goal of this problem is to design a system such that it has the following specification for a ...
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### What sampling frequency should I use if Nyquist is not available?

I have the following homework question that confuses me: We have an audio emitter that can emit two signals: It either emits a sine wave at 23 kHz or it emits a sine wave at 25 kHz. The receiver has ...
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### Fourier Transform of the conjugate of a complex function [closed]

Given that $x(t)$ Fourier Transforms to $X(f)$. What happens when you Fourier Transform $x^*(t)$, and your $x(t)$ and $x^*(t)$ are both complex functions??
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### Impulse response $h[n]$ of a non linear I/O equation

my question concerns an assignment that was given to us at school. We have been given a list of I/O equations and it is required, for each of them, to find the impulse response $h[n]$ and the ratio ...
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1 vote
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### Find $A$ and $G$ value to satisfy the requirement

Given a disturbance reduction system Create a system that will reduce $U(s)$ noise to $100$ times its value. Find the A and G gain value to satisfy the requirement My attempt: I've analyzed the ...
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### Unit step function symbol

I've been studying communications and i see that the book used the symbol $u_{-1}(t)$ for unit step function , why ?
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### Does $\cos(bt)\cdot u(t)$ have a Fourier Transform?

If it does, $$\int_{-\infty}^{\infty} \cos(bt)\,u(t)e^{-j\omega t} dt = \int_{0}^{\infty} \cos(bt)\,e^{-j\omega t} dt = \int_{0}^{\infty} \frac{e^{jbt} + e^{-jbt}}{2}\,e^{-j\omega t} dt$$ Then how do ...
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### Confused with using Fourier Transform Properties

I'm seeking the Fourier transform of $t \cdot (u(t+1)-u(t-1))$ Given the fact that (The first minus here should be a plus) Using properties. My initial approach was: but I wasn't sure how I should ...
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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 ...
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### 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 :- $$S(t) = 5\cos(10πt - π/2) + 3\sin(30πt)\qquad \textrm{[Using \sin(2A) = 2\sin(A)\cos(A)]}$$...
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### 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 ...
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1 vote
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### 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 ...
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### 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
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### 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) ...
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### 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 ...
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### 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 ...
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### 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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### Is this an energy or power signal?

Is the given input signal x[n] an energy or power signal? The image shows what I did so far. Is it correct? Thank you! EDIT: I solved it again, please tell me if I did it correctly this time. E= \...
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Homework Question: Consider a signal $x[n]=\alpha e^{j \omega_{0} n}+\beta e^{j \omega_{1} n}+\gamma e^{j \omega_{2} n} .$ What is the length of impulse response $h[n]$ of a system (non-trivial) such ...
Consider a signal x[n] and its DTFT $X(e^{jω})$ . Assume $X(e^{jω})$ is differentiable. Compute the inverse DTFT of $j\frac{dX(e^{jω})}{d\omega}$ You should write your answer in terms of $x[n]$ and ...