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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Plotting the Frequency Response of Zero-Order Hold

I'm trying to find the frequency response and the DC gain, then plot the response and find the cutoff frequency from the graph. I start off with the impulse response $$h(t)= 1 ; 0\leqslant t\leqslant ...
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1 vote
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Labels in speaker verification

I'm a beginner. If I am using a Convolutional Neural Networks with Triplet Loss as a loss function (also combined with GAN and a Classifier) for building a model that performs Speaker Verification, ...
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How to calculate the DFT for this sum of cosine's in the form $\sum A_i \cos(\omega_i n + \phi_i)$ for fixed $N$

I am stuck trying to calculate the DFT for a given $N$ Given the signal $x[n] = \cos(\frac{\pi}{2}n - \frac{\pi}{2})+2 \cos(\pi n + \frac{\pi}{2})$ and $N = 4$ I tried to calculate the DFT $X[k] = \...
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1 answer
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Fourier Series of a piecewise function

I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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1 answer
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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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2 answers
55 views

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 ...
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1 vote
1 answer
88 views

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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2 votes
1 answer
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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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19 votes
3 answers
3k views

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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1 answer
111 views

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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-1 votes
1 answer
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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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Running a signal through a circuit with some odd components

I am studying a course in signal analysis and systems. Currently we are looking at aliiasing, samplig,DTFT and reconstruction. I got stuck on an excercise. For the in signal $x_{a}(t)=2\cos(2\pi F_{0}...
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1 answer
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FInd the amplitude function to a system

I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky. I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
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Zeroes and poles for a system

I have run into some issues on an exercise for the course in signal analysis and systems I am currently studying. We are to create an echo effect and are using the system below: I am to find the ...
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3 answers
77 views

Noise variance estimation under known channel

I have $N$ observations $\{y_i\}_{i=1..N}$ $$y_i = h_i x_i + w_i$$ where $\{x_i\}_i$ are the realizations of uniform distributed QPSK symbol $x$, i.e. $x_i \in \{\pm\frac{1}{\sqrt{2}} \pm j\frac{1}{\...
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1 vote
1 answer
88 views

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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1 answer
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Finding transfer function from bode plot

Given a bode diagram From the figure, I see that when $\omega = 100 \text{ rad/s}$ the magnitude response starting to go down and when $\omega = 1000 \text{ rad/s}$ the slope become higher. Then $$H(...
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A discrete time signal $x[n]$ is defined in terms of unit impulse function.Express the signal $x[n]$ in terms of step signal

A discrete time signal $x[n]$ is defined in terms of unit impulse function as follow $$x[n]= 1-\sum_{r=3}^\infty \delta[n-1-r]$$ If $x[n]$ is expressed in terms of unit step function as $x[n]=u[an-b]$ ...
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-1 votes
1 answer
82 views

Find response of discrete time LTI system given input and impulse response

For this question the guide says to use $Y(e^{j\omega}) = H(e^{j\omega}) X(e^{j\omega})$. I have been able to find the discrete time Fourier transform of the impulse function as $$H(e^{j\omega}) = \...
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1 answer
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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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1 answer
126 views

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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  • 267
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1 answer
72 views

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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  • 267
1 vote
0 answers
123 views

Finding original signal $x(t)$

For given 4 conditions, I have to find out what is $x(t)$ with period of 3, and I don't know if $x(t)$ is real or not. For fourier coefficients $x_k$, $$1.\ x_k=x_{k+2}$$ $$2.\ x_k=x_{-k}$$ $$3.\ \...
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3 votes
1 answer
71 views

Understanding LTI systems graphically

I'm currently working on this problem from Oppenheimer's book: Given $x_{1}(t)$ and $y_{1}(t)$ I should figure out $y_{2}(t)$ and $y_{3}(t)$ given that the system is LTI. My progress so far: I'm ...
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  • 267
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3 answers
236 views

How do I check for linearity for the following piecewise-defined system?

The problem at hand: Where I'm currently stuck: I'm not entirely sure about how to move on from this point, I'm trying to find the superposition of the responses of the two individual signals so I ...
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2 answers
278 views

Inverse Fourier Transform of piecewise function

Objective : Compute $y(t)$ from $Y(j\omega)=H(j\omega)X(j\omega)$ where : $$ x(t)=\left(\frac{\sin(2t)}{\pi t}\right)^{2} $$ and $$ H(j\omega)=\begin{cases}e^{-j\omega}&\text{if $|\omega|<4$}\\...
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2 answers
753 views

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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0 votes
1 answer
39 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 :- $$S(t) = 5\cos(10πt - π/2) + 3\sin(30πt)\qquad \textrm{[Using $\sin(2A) = 2\sin(A)\cos(A)$]}$$...
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2 votes
1 answer
87 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 ...
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1 vote
1 answer
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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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0 votes
2 answers
44 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 ...
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1 vote
3 answers
1k 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) ...
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0 votes
1 answer
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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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0 votes
1 answer
572 views

Find the autocorrelation function of signal $x(t) = u(t) - u(t-1)$

I have used the energy-type signal autocorrelation function: $$\mathcal{R}_{xx}(\tau)=\int_{-\infty}^{\infty}x(t)x^*(t+\tau)dt$$ I have rewritten the equation as: $$\begin{align} \int_{-\infty}^{\...
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4 votes
3 answers
1k views

Is this system causal or not?

My efforts of solving this question are below. I came to a conclusion that this system is causal, since: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
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1 vote
1 answer
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MIT 6.003 HW#8 Problem 4 - Fourier Coefficients of Triangle Wave

In the mentioned homework, part of the solution involves finding the Fourier coefficients of the triangle wave. The solution mentions that we can express this function as follows: What does that ...
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2 votes
2 answers
1k views

Find power of a sum of sinusoids

We got this question to solve: Calculate the power of the signal: $$s(t) = 8\cos\left(20\pi t-\frac \pi4\right) + 4\sin(15\pi t)$$ Now, I thought of two approaches : Use Parseval theorem, so first ...
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0 votes
1 answer
95 views

Determine if system is linear time variant

The system equation is given as: $$y(n)=(n-1)x(n-1)+(n+1)x(n+1)$$ I solved that the system is time variant: \begin{align} y(n-k)&=(n-k-1)x(n-k-1)+(n-k+1)x(n-k+1)\\ H[x(n-k)]&=(n-1)x(n-k-1)+(n+...
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0 votes
2 answers
52 views

Convert complex valued sinusoid to real valued sinusoid

This is the homework problem: convert $x[n]=je^{j\pi n/8}-je^{-j\pi n/8}$ to a real valued sinusoid. I understand that $\sin\theta=\dfrac{e^{j\theta}-e^{-j\theta}}{2j}$ In the solution, the answers ...
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0 votes
1 answer
61 views

Linear systems: Square root of input product

Hi guys i'm studying signals and systems, and my professor ask us if this signal is linear or not $$y(t) = \big[x(t − 1)x(t + 1)\big]^{\frac 12}$$ the fact that is in the form of $x\cdot x$ told me ...
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2 votes
1 answer
139 views

Confusion for two-sided signal

Given a continuous LTI system with transfer function $$H(s)= -\frac{2s}{(s+6)(s+2)}$$ Plot the location of the pole(s) and zero(s) Find all possible regions of convergence From the problem above find ...
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0 votes
2 answers
140 views

Determining Causality and Time-Invariance of a system

Consider the following system: $$y(t-1)=\int_{-\infty}^\infty x(𝜏)u(𝜏-t) d𝜏 $$ where $u(t)$ is the unit step function, which is zero for $t<0$ and equals $1$ for $t>0$. $(1)$ Is the system ...
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-1 votes
1 answer
78 views

Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF

I would like to raise a mathematical question : Let's say we are been given : $$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\ 0 & \textrm{otherwise} ...
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-1 votes
1 answer
228 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 ...
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-2 votes
1 answer
121 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 ...
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1 vote
2 answers
461 views

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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2 votes
1 answer
273 views

Find the length of the impulse response for the given output and input

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 ...
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0 votes
1 answer
72 views

Inverse discrete time Fourier transform with differentiation

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 ...
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