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1answer
95 views

Bounds on least squares and weighted least squares estimator

I was wondering if I can get some help in getting bounds on the parameters estimated by least squares (LS) and weighted least squares (WLS) methods. Suppose our observation model is: $\mathbf{y} = \...
1
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1answer
133 views

Fourier transform of a signal sequence?

Desparately, I am trying to calculate the Fourier transform of the following signal sequence. What can it be? $$f(x)=\left(\frac{\sin(\pi x)}{x\ln(T)\sin[\pi\ln(x)/\ln(T)]}\right)^2$$ while $x > ...
2
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0answers
102 views

Proof of Caratheodory's theorem about the unique determination of a linear combination of sinusoids

Following is a statement of Caratheodory's Theorem about a positivelinear combination of sinusoids :- Any positive linear combination of k sinusoids is uniquely determined by its value at time t =...
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1answer
97 views

Signal compression

I believe I have an extremely simple question but I can't seem to figure it out. This image shows $x[n]$ and I have to draw $y[n]=x[2n-4]$ by first doing a compression and then a time shift. The ...
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0answers
286 views

Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
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3answers
811 views

Bases in compressed sensing (signal reconstruction)

I have been posting this kind of question in Cross Validated, but since this one deals almost entirely with mathematics, I will post it here. In signal reconstruction using compressed sensing, we ...
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2answers
293 views

Given one sine wave in time domain, how to find its frequency?

Given one sine wave in time domain, I want to find its frequency. Because I observe only a very small part of the sine wave ~1 cycle, FFT methods have a poor spectral resolution. Has there been work ...
3
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2answers
1k views

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
2
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1answer
591 views

Using FFT in matlab

I am not completely sure if this is where a MatLab question belongs, so if not, please direct me where I should ask. But onto my question. I am working on trying to deconvolution a signal with noise....
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1answer
890 views

Approximation of Saturation function

"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1) The context where I encountered this is LTI (linear time-invariant) system analysis (in classic ...
2
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1answer
98 views

What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: public double[] calculateARCoefficients(double[] inputseries, int order) When this method ...
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2answers
69 views

Max frequency of a signal?

Having $$ f(x) = \cos(x) + \sin(10x)$$ How Can I know which is the max frequency of this signal? I need it to set the right Nyquist frequency ($2\cdot\max\text{frequency}$) I can use Matlab if it'...
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1answer
437 views

Sawtooth wave spectrum

Could a good soul help me? I heard that the fourier transform of a periodic signal is a pulse train, but for a sawtooth wave: what is the fundamental frequency of the spectrum? Thanks
3
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2answers
943 views

How do I find transfer function of a discrete-time system when its state-space form is given?

I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case. For example, given the state-space equations of the second ...
0
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1answer
359 views

Find peak output value using transfer function

I have a filter with Transfer function $H(z)=(1-0.5z^{-1})(1+0.5z^{-1})$ designed for a sampling rate of 800 samples/s. How to find peak output if a sine of 200Hz and amplitude 4 is applied as input?
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1answer
77 views

Transfer Function from input to node.

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node: The circles contains 'X' inside are multiplications. The circles contains 'Σ' inside ...
2
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0answers
89 views

Why process noise model is$ \dfrac{T^4}{4}$ in Kalman filter.

I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2: $$ s \times s = \dfrac{T^2}{2} \...
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1answer
70 views

Find the transform

I have the paper with 3 points on it. I have also a photo of this paper. How can I determine where is the paper on the photo, if I know just the positions of these points? And are 3 points enough? It ...
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1answer
114 views

Signal approximation using linear combination of functions

How I can approximate the signal $x(t)=0.001\,t^3 \exp(-0.1t)$ in the interval $[0,100]$ using a linear combination of the following functions: $f_1(t)=A_1$ $f_2(t)=A_2\cos(0.05t)$ $f_3(t)=A_3\cos(...
2
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2answers
4k views

What is the inverse z transform of 1/(z-1)^2?

I'd like to know how to calculate the inverse z transform of $\frac{1}{(z-1)^2}$ and the general case $\frac{1}{(z-a)^2}$
3
votes
2answers
902 views

Problem with Discrete Parseval's Theorem

I think I must be missing something obvious, but I can't for the life of me see what it is. The discrete version of Parseval's theorem can be written like this: $\sum_{n=0}^{N-1} |x[n]|^2 = \frac{1}{...
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1answer
334 views

Mathematically inclined books on Signal Processing Theory

First off, i know this may seem off topic but i could not find help in signal processing communities so i was hoping there would be people here who both love mathematics and have interest in signal ...
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2answers
2k views

Scale Space - Scales and Octaves

So I'm desperately trying to understand scale space for signals, specifically for 2D images... I'm having trouble with algorithms that discuss creating a pyramid. Specifically, I don't understand how ...
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1answer
31 views

How to show quantisation error for frequency coefficient

I have the following question from an exam which reads: For the second question my answer is: 24 5 2 3 9 2 1 3 2 3 2 2 1 1 1 0 I am unsure of what formula ...
5
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2answers
129 views

partially reconstruct information of function convoluted with boxcar kernel

the function (f) I want to reconstruct partially could look like this: The following properties are known: It consists only of alternating plateau (high/low). So the first derivation is zero ...
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1answer
120 views

Nyquist criterion

When using the Nyquist stability criterion, amplitude-frequency characteristic etc. we go from the Laplace image $G(s)$ to $G(j\omega )$. By definition of the Laplace transform, $s=\sigma + j\omega$. ...
2
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2answers
406 views

I need to calculate the period, I need help to verify my answer

I need to determine if $x(t) = 9\cos(2t) + 4\sin(\pi t)$ is periodic. If it is periodic I need to find the period. this what I have done \begin{align*} T_0 &= 2\pi/w\\ T_1 &= 2\pi/2 = \pi \\ ...
4
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2answers
633 views

Is the convolution an invertible operation?

If I have a signal $f(x,y)$ (discrete) and I convolve this signal with a kernal $h(x,y)$: $y(x,y) = f(x,y) \star h(x,y)$ (where $\star$ is the convolution operator) Can I obtain $f(x,y)$ given only $...
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1answer
50 views

Extracting independent sources from available signals.

I have four signals in time domain, in the format of 4 vectors (a,b,c,d). I know there are 3 sources contributing these signals. One is a source that is shared between all four signals. One is a ...
2
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0answers
325 views

Checking if (discrete) signal is stationary, BIBO stable and

I have this discrete signal y[n] = sum (x[k+1]h[k-1]), where k goes from -inf to +inf. I need to check if this signal is stable, stationary, and if it's invertible, i need to find it's inverse ...
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0answers
501 views

How can I find the compact trigonometric Fourier series from these signals?

I've been stuck on this for a while, but how exactly would I go about calculating the compact trigonometric Fourier series for both of these signals? I have a general formula down for it, but I just ...
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2answers
227 views

Complex expression for periodic binary sequences

We have infinite binary sequences of type $$\langle g_n \rangle_{j=4}=\{0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,...\} \,;\, n\to\infty$$ where $j$ indicates the length of a period that starts/ends with a $1$; ...
2
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1answer
90 views

FFT for a single frequency

I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
2
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1answer
388 views

Check the orthogonality of two functions

This is a part of two Passband Signals. My question involves inner product. Is $$ \left < \cos(2\pi ft + \phi) , \sin(2\pi ft + \phi) \right> $$ where $\phi \in [-\pi, \pi)$ equal to zero, i.e. ...
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1answer
1k views

solve an difference equation's particular solution with unit step input

I have a question like this $y[n] - \frac 2 5y[n-1] = 2x[n]$ and $x[n] = 2u[n]$, the manual say that $y^p[n] = k u[n]$ and subtitute it into the equation will become $ k - \frac 25k = 4$. But I think ...
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1answer
608 views

How can I calculate the bode magnitude and frequency as well as their plots?

I've been trying to figure this problem out for a while now. I've been given a transfer function $$H(s) = \frac{s(s+100)}{(s+2)(s+20)}.$$ I'm supposed to calculate the bode magnitude and frequency for ...
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0answers
57 views

Discrete time fourier transform of partial sum

I came across the following property of the DTFT: $ \mathcal{F} \Bigg(\sum_{m=- \infty}^{n}x[m]\Bigg) = \frac{1}{1- e^{-j \omega}} X(e^{-j \omega}) + \pi X(e^{-j0}) \sum_{m= -\infty}^{\infty}\delta({\...
3
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1answer
13k views

Prove of the Parseval's theorem for Discrete Fourier Transform (DFT)

If $x[k]$ and $X[r] $ are the pair of discrete time Fourier sequences, where $x[k]$ is the discrete time sequence and $X[r]$ is its corresponding DFT. Prove that the energy of the aperiodic sequence $...
0
votes
1answer
96 views

Find the non null complex Fourier coefficients

I'm doing my homework on signal processing in MatLab and I'm stuck on an exercise. I'm given this signal $x(t)=1 + 2\sin(12\pi t+\frac{\pi}{4})\cos(21\pi t);$ and I have to get the non null complex ...
0
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1answer
165 views

The science of pearson product moment correlation coefficient

I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the ...
2
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2answers
59 views

Express $\cos(5t)$ with the help of Euler formula

I can't figure out, how to express $\cos(5t)$ in the form $e^{j\omega t}$. I don't even know the right answer. How would you deal with this task?
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2answers
63 views

How does one verify if a vector is really recovered?

In compressed sensing, how to verify if a vector is really recovered or how does one plot the figures on recovery rate? Since in numerical experiments, there is always a difference between the ...
1
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1answer
188 views

How to determine the function of this “black-box”?

Imagine a black box which accepts a digital input signal which is a pure sine wave and outputs the area between this input signal and some constant data set over a sample window. Given the input ...
0
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1answer
140 views

response impulse function

my question is related to time series modeling in signal form,i have such question,suppose we have time series data $y_1........y_n$,how can we represent in impulse response form?as i ...
3
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1answer
575 views

Find the expression and the system impulse response

I've started to learn signal fundamentals and I have to do one exercise and I can't understand something. It is said that $$x[n]=1.5\cos(0.025 \Pi n)(u[n+40]-u[n-40]))$$ and that the signal $u[n-m]$ ...
2
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1answer
1k views

Relationship between DFT index values, frequency in a Fourier series and Hz.

I have a sound file recorded at 44.1 K samples per sec, and some FFT and IFFT algorithms. The sound file is a vector with about $ 2^{17} $ elements. My objective is to find which of the index values ...
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0answers
188 views

Pre-Emphasis of a signal

I'm trying to describe the process of Pre-Emphasis (of a signal) in my equations, but I don't know whether or not this makes sense. $Y[n] = X[n] - 0.95 \cdot X[n-1]$ Where Y = pre-emphasis after, X ...
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1answer
121 views

Discrete time signal and unit step

I've started to learn signal fundamentals and I have to do one exercise and I can't understand something. It is said that $$x[n]=3\cos(0.1 \Pi n)(u[n+55]-u[n-55]))$$ and that the signal $u[n-m]$ is a ...
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1answer
4k views

How to determine the step response using convolution of the signal's impulse response?

The step response can be determined by recalling that the response of an LTI to any input signal is found by computing the convolution of that signal with the impulse response of the system. ...
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1answer
91 views

Finding two highest peaks in a chunk of samples

Supose I have a list of 600 samples of numbers, and the histogram of the samples looks like the following: As can be seen, there are two 'mountains' of values around 16 and 48, and a outlier in 95. ...