Questions tagged [cosine]
The cosine tag has no usage guidance.
56
questions
0
votes
0
answers
26
views
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 ...
- 1
0
votes
0
answers
41
views
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-...
- 345
2
votes
1
answer
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 ...
- 296
0
votes
1
answer
59
views
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 ...
- 345
3
votes
1
answer
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 ...
- 223
0
votes
0
answers
74
views
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 ...
- 3
2
votes
2
answers
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 $l^{th}$...
- 345
0
votes
1
answer
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 ...
3
votes
1
answer
1k
views
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 ...
- 293
0
votes
0
answers
29
views
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 $m(t)=a\cdot\cos(2\pi f_c t)$.
- 23
1
vote
1
answer
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
0
answers
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 ...
- 11
-1
votes
1
answer
64
views
Filtering a sum of cosines
The block diagram below represents a linear modulation system operating at the frequency of $1000 Hz$, $f_C = 1000 Hz$, transmitting the message $m(t) = 2\cos(400πt)$
At point B, i got the signal: $$...
- 13
-1
votes
1
answer
72
views
What type of data need to be used for multiplication of sine and cosine signals in mixer?
I want to multiply sine and cosine signals(have same frequency).
I've sampled the signals and converted to digital .
Samples can range from 0 to 4096.
like 4095, 4078, 4028, 3945, 3832, etc...
I want ...
- 23
1
vote
3
answers
433
views
Unexpected imaginary part in the fft of a zero-padded cosine
I simulated a cosine waveform $ y = \cos(\omega t) $ and I applied the FFT algorithm to it. As expected, I have a frequency peak at $\pm \omega$ only in the real part, and nothing in the imaginary ...
- 119
3
votes
2
answers
948
views
DTFT of sine wave using freqz
As mentioned in the title, is it possible to use freqz to find the DTFT of a sine wave? I am confused about what the 'a' and 'b' vectors would look like, since there are only impulses in the numerator....
1
vote
1
answer
291
views
Setting up RRC filter and useful equations
I have looked at previous answers but cant seem to get everything I need in one place to help me and my textbook doesnt explain this in practical terms.
Signal Parameters:
$F_s = 44100$
$R_s = 300$
$...
- 452
0
votes
1
answer
121
views
Discrete time sine wave generation near nyquist
I'm trying to wrap my head around how to generate sine-waves out of a DAC near the Nyquist frequency (or determining how close I can get for reliable results). So if I want to generate a 499 Hz sine ...
- 201
1
vote
1
answer
52
views
Optimization of harmonics calculation
I need to compute the sine and cosine of an argument along with n "harmonics"
\begin{matrix} \sin(x) & \cos(x) \\
\sin(2x) & \cos(2x) \\
\cdots \\
\sin(nx) & \cos(nx)
\end{...
- 3,735
0
votes
2
answers
627
views
Ideal low pass filter output at given sampling frequency
Consider the signal $\cos(30t)$ sampled at $w_s=40 rad/s$ using a unit impulse train. The sampled signal is filtered with an ideal low pass filter with unity gain and cutoff frequency $w_c = 40rad/s$. ...
1
vote
1
answer
660
views
Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$
Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$
I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I don’t know how ...
- 174
1
vote
1
answer
358
views
time scaling and shifting of cosine in Fourier transform
I've met some problems when calculating the Fourier transform of $\cos(at+b)$. I want to use the shifting and scaling properties to solve this problem. First, when I look up in the book and some ...
- 13
1
vote
3
answers
401
views
Nyquist Rate of cosine modulated function
Here's my understanding:
$$y(t) = x(t)~ \cos(\Omega_0 t)$$
I take the Fourier transform of y(t) and I get this result:
$$Y(\Omega) = \frac{1}{2}X(\Omega - \Omega_0) + \frac{1}{2}X(\Omega + \...
- 193
4
votes
2
answers
377
views
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 ...
- 331
0
votes
1
answer
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.
...
- 141
0
votes
1
answer
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 ...
- 183
2
votes
5
answers
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 ...
- 141
0
votes
2
answers
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 ...
- 141
0
votes
1
answer
291
views
When can a windowed cosine be considered band-limited signal?
I have an exam in the following days and i have no clue of what is the response to this question in the exam:
given this signal:
$$g(t) = H\left(t+\frac{T}{3}\right) f(t) - H\left(t-\frac{2T}{...
1
vote
1
answer
128
views
Amplitude modulation in pure sine wave [duplicate]
I am generating sine wave in MATLAB with following code
...
- 113
2
votes
2
answers
141
views
How would one design a (quasi) linear phase adaptive notch filter for a single complex tone?
While IIR notch filters are attractive, I need to retain phase linearity at the filter output. I imagine that it's possible to use a standard IIR notch filter:
https://www.researchgate.net/...
- 375
3
votes
1
answer
508
views
What are the cosine functions in JPEG's DCT-II table?
As I understand it from this video, in a JPEG image an 8x8-pixel block is made up of weighted cosine waves, calculated using DCT-II. There are lots of visualizations of these waves, such as this one ...
- 133
0
votes
1
answer
114
views
Sum of cosines as squashed as possible
I have 10 cosine waves of the form $\cos(2\pi(x f_n+\varphi_n))$, where $f_n$, the frequency, is an integer from 1 to 10 and $\varphi_i$, the phase, is a number from 0 to 1:
$$s(x) = \sum\limits_{n=1}...
- 119
0
votes
3
answers
303
views
"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 ...
- 1,107
8
votes
1
answer
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). ...
- 13.5k
-1
votes
1
answer
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 <...
- 117
0
votes
1
answer
753
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:
...
- 137
0
votes
2
answers
52
views
How to make sure that a sinusoid wave with different subsequent frequencies matches up?
A very basic formula to transform a sequence of notes into a signal would be:
$$
x(t) = A\cos( 2 \pi (2^{current\_note}/12) t)
$$
where $current\_note$ is $notes[\lfloor t / period\_per\_note\...
- 105
1
vote
2
answers
67
views
Rearranging exp terms
I have some problems rearranging exp terms to receive a cos or sin. I guess the solution is silly but I‘m not able to spot my mistake.
I know the solution (since i looked it up with wolfram alpha) ...
- 328
4
votes
1
answer
934
views
Bridging CTFT and DTFT for a cosine
I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT.
For example if I take a basic example:
$$\begin{aligned}
x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
- 145
1
vote
2
answers
704
views
Fourier series of $cos(\omega_0 t)$ in continuous time
Can any one please help me with understanding how we can calculate the Fourier series of Cos(w0t) using the formula:
I saw that they did the following calculus, but I Don't really understand how we ...
- 61
2
votes
1
answer
1k
views
Why MATLAB fft cos makes imaginary parts?
The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little big.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(7);
fs=128;
t=-4*pi:1/fs:4*pi-1/fs;...
- 59
0
votes
1
answer
119
views
Extracting a DC value from a sum of sinusoids
I guess it might be a basic questions but here it goes anyways.
How could I extract a DC value from a sum of sinusoids, i.e.:
$$v(t) =\widetilde{v_{dc}} + \sum_{n=1}^{\infty}\sin(\omega_nt+\phi_n)$$...
- 175
8
votes
3
answers
2k
views
Replacing "e" in Euler's formula with another number
Does Euler's formula remain valid if we use any real number other than the constant $e$? For example replacing $e$ with 5 would make the formula look like this: $5^{it}$.
I tried this idea in ...
- 81
0
votes
1
answer
281
views
How does the 'phase' of a cosine wave become 'pi' when it transitions from positive to negative?
I was watching this video lecture on filters where this professor says that:
The phase of a cosine wave $\cos(\omega)$ is 0 till $\omega=\pi/2$. As soon as $\omega$ goes beyond $\pi/2$, i.e when $\...
- 159
0
votes
1
answer
2k
views
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 ...
- 317
2
votes
1
answer
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 ...
0
votes
2
answers
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
2
answers
3k
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 ...
- 317
1
vote
1
answer
170
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 ...
- 53