# Questions tagged [cosine]

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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 $m(t)=a\cdot\cos(2\pi f_c t)$.
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### Transform fourier a cos wave [duplicate]

I have this $\cos(100\pi t)$ or $\cos(100\pi t)$ wave. How can I Fourier-transform this function? One of my thoughts is that $π[ δ(f-100)+δ(f+100)]$. So the transfer is good or wrong?
1 vote
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### 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
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### 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 ...
60 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. ...
172 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 ...
2k 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 ...
206 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 ...
334 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). ...
348 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 <...
512 views

### 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 ...
99 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
2k views

### Moving Average of sinusoid

If you calculate a simple moving average over a window length that is equal to the period of the sinusoid, you get a straight line (=0 because the wave is symmetric around the X-axis): the wave has a ...
1 vote
121 views

### How would Fourier and Cosine Transforms responds to summation of cosines with same frequency but different phases?

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 ...
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### Sine wave phase shift from Fourier Transform

This is probably a really basic question but I'm a little stumped and would appreciate some practical input on how to go about doing this rather than reading dockets of equations semi-related to what ...
1 vote
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### recovering phase of sine signal from FFT

I have a simple sine function as $sin(2\pi ft + \phi)$. I want to obtain the phase signal $\phi$. I tried to use FFT to calculate $\phi$. In matlab I do the following ...
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### For discrete signals, why does phase change not correspond to time shift?

I'm going through a Signal Processing lecture where the professor mentions this fact and the argument given is: Suppose you have a sinusoidal signal: $Acos(\omega t)$ Now if you change the phase of ...
1 vote
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### Validating cross corrolation between sine and cos, shouldn't pahse lag be pi/2?

I am trying to use cross correlation instead of FFT to find lags between 2 signals. I am trying to understand cross correlation by using it on sin and cos and expecting phase lag to be pi/2 but it is ...