# Questions tagged [cosine]

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### Beginner help with raised cosine graph of impulse in Matlab

Hi I'm looked to graph a Raised Cosine Bell Curve according to ones similar presented in the linked article. I have no experience with MatLab, and have found little luck scowering this and other sites ...
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### What is the possible application of eigenvalues?

I am a PhD in mathematics. Recently, we made an attempt to compute the eigenvalues of non-normalized discrete sine and cosine transforms. Surprisingly, the issue regarding three particular types, DCT-...
130 views

### Why is there a difference in the phase when using fft versus a manual DFT on a cosine signal?

Apologies if this is a duplicate, but I can't find a good answer anywhere. If I have a time-domain cosine signal of the form: $$x(t) = A\mathrm{cos}(\omega_0 t)$$ Then this will result in an Fourier ...
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### The benefit of Eigendecomposition of DCT and DST

I am Ph.D in pure mathematics and interested in signal processing. Theoretically, any illustration of the eigendecomposition of the discrete trigonometric transforms (DTTs) is worthwhile. Q. What real ...
105 views

### Error in complex signal with imperfect quadrature phase and amplitude (textbook question)

I am working on the following problem: I have a solution that I am pretty confident is correct as have checked the output in python. However, it is long and the entire time I was answering the ...
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### How do I match a filter to an AWGN channel?

I have the task to find a transition that fulfills the first Nyquist Criterion. After that I am supposed to match that filter to an AWGN channel. For the first part I thought a raised cosine ...
92 views

### An new arranging of the discrete Sine transforms

Let $n$ be even and consider the non-normalized discrete Sine transform of type 5 which is $$S=\left(\sin(k+1)(l+1)\frac{\pi}{n+\frac12}\right)_{k,l=0}^{n-1}$$ Let us denote $s_{-,l}$ by the $l^{th}$...
39 views

### Strange Look to Sampled Sinusoid [duplicate]

Ok so as part of a project for school I have been designing an FIR bandpass filter. The output should have been a signal which looks like a sampled sinusoid but there was a strange alteration on the ...
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### Envelope detection using hilbert transform

I have a sine wave of frequency 1kHz sampled at 16kHz. I need to find the envelope of this signal using hilbert transform in MATLAB.I have used the inbuilt function abs(hilbert(input_signal)) and got ...
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### How to create a signal m(t)?

I have this signal $m(t)=8\sin(9\pi t)\sin(8\pi t)$, my teacher gave as explain $2\sin x \sin y=\cos(x-y)-\cos(x+y)$. So how to create and get this signal $m(t)=a\cdot\cos(2\pi f_c t)$.
1 vote
166 views

### Integration of Sinusoidal functions

Since Differentiation of a sinusoidal function of a certain angular frequency gives a sinusoidal function of the same frequency, does the statement "Integration of a sinusoidal function of ...
1 vote
94 views

### Z-transform of $\cos(\omega_0 n(n+1))u[n]$

I'm doing some research on Zadoff-Chu sequences and as a part of it I wanted to find the Z-transform of: $$\cos(\omega_0 n(n+1))u[n]$$ Wolfram Alpha / Mathematica couldn't help out. I couldn't find a ...
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### Running Integral of sine and cosine functions

In typical signal processing course we were taught that the integral of signal $x(t)$ is given by $$y(t) = \int_{-\infty}^{t}x(\tau) d\tau$$ How can we use this definition to evaluate the integrals of ...
88 views

### harmonic waves as integer multiple in spectrum

i have a motor that is rotating with a certain frequency. If i check the frequency spectrum it contains a peak on 150 hz. Also i have peaks at 300,450,600 ... i guess that those peaks are harmonics. ...
499 views

### Difference between frame rate and sampling rate?

Below are the two different methods of generating time to create an audio sine wave. While framerate is being used as steps in one method, the inverse of sampling rate is being used as steps in the ...
3k views

### A question about sampling rate of cosine signal

Given $$c(t) = \cos(2\pi\cdot 30 \cdot t)$$ If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following: There is no aliasing as $f$ = 30 Hz is less than ...
538 views

### Sampling $x(t)=\cos(4\pi t)+\cos(2\pi t)$

Imagine that we sample the signal $x(t)=\cos(4\pi t)+\cos(2\pi t)$ with a certain sample frequency $f_s$ and we obtain $x[n]$. Now, by ideal interpolation, we get $y(t)$ from $x[n]$. How can we know ...
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### "Sinusoidal" in DSP terminology

This is probably a bad question but I'll ask anyway because I'm often confused by it. Many textbooks explain how the movement of $z$ around the unit circle can be broken up into a sine wave along the ...
383 views

### Optimal amplitude of an $m$-bit sinusoid

A continuous-time sinusoid of zero-to-peak real amplitude $A \le 2^{m-1}-0.5$ (e.g., for $m=16$, $A \le 32767.5$) is quantized to $m$-bit resolution by rounding it to the nearest integer (Fig. 1). ...
406 views

### Displaying Cosine Signal in Python [closed]

I am new to signal processing concept, so this can be easy question. Actually, I want to display cosine signal by using python scipy.signal module. The method <...
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### How do I find the frequency of a particular bin in a cosine transform, and two other questions

I have a discrete series of values and I have applied a Discrete Cosine Transform to it, obtaining values like: ...
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### Combining 2 sinusoids of equal amplitude with different frequencies into 1 new "wave"

This question is about combining 2 sinusoids with frequencies $\omega_1$ and $\omega_2$ into 1 "wave shape", where the frequency linearly changes from $\omega_1$ to $\omega_2$, and where the wave ...
1k views

### Linear prediction (LPC) of Sine wave samples around maximas

I think I missed class when this was explained ... Anyway as part of a bigger project I have to implement a LPC to predict 2-3 future values of a sinusoidal process. I wrote a small Matlab m-file to ...
107 views

### Simulating spatial perception - with cosine wave based sound - in MATLAB

I'm trying to create cosine wave, one for the right channel and another for the left. The one on the left is to be moved in phase to simulate change to the spatial perception of the tone. A delay in ...
1 vote
For example, if I have two signals, $\cos(2\pi ft+\frac\pi4)+\cos(2\pi ft+\frac\pi3)$, what would be different in both transforms (Fourier and cosine) how would the spectrum changes? And What would ...