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what will be the expression of this shifted cosine signal

My solution is $y(t) = \cos(\omega t) + \frac{1}{2}$ giving it a shift of $\frac{1}{2}$ But I'm a bit skeptic about it, should there be any coefficient of cos to this modification?
Wireshark's user avatar
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0 answers
30 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 ...
greein20's user avatar
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0 answers
44 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-...
ABB's user avatar
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2 votes
1 answer
186 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 ...
Darcy's user avatar
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0 votes
1 answer
61 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 ...
ABB's user avatar
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3 votes
1 answer
119 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 ...
Joseph's user avatar
  • 223
0 votes
0 answers
93 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 ...
Ole's user avatar
  • 3
2 votes
2 answers
94 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 $l^{th}$...
ABB's user avatar
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0 votes
1 answer
40 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 ...
RickarySanchez's user avatar
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 ...
Aami's user avatar
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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 $m(t)=a\cdot\cos(2\pi f_c t)$.
Lilfio's user avatar
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1 vote
1 answer
200 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 ...
Mathpdegeek497's user avatar
1 vote
0 answers
113 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 ...
Eduards's user avatar
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-1 votes
1 answer
65 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: $$...
carraro's user avatar
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-1 votes
1 answer
76 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 ...
user653241's user avatar
1 vote
3 answers
487 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 ...
DrManhattan's user avatar
3 votes
2 answers
1k 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....
Pranav Krishnan's user avatar
1 vote
1 answer
408 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: $F_s = 44100$ $R_s = 300$ $...
Natalie Johnson's user avatar
0 votes
1 answer
199 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 ...
Sittin Hawk's user avatar
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{...
Ben's user avatar
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0 votes
2 answers
746 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 $w_c = 40rad/s$. ...
alir0b0t's user avatar
1 vote
1 answer
764 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 ...
Vitali Pom's user avatar
1 vote
1 answer
432 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 ...
Peter24's user avatar
  • 13
1 vote
3 answers
469 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 + \...
pico's user avatar
  • 203
4 votes
2 answers
395 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 ...
user5045's user avatar
  • 331
0 votes
1 answer
98 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. ...
Khan's user avatar
  • 141
0 votes
1 answer
674 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 ...
Sachin's user avatar
  • 183
2 votes
5 answers
4k 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 ...
Morcus's user avatar
  • 141
0 votes
2 answers
608 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 ...
Gibbs's user avatar
  • 141
0 votes
1 answer
327 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}{...
Dario Formi's user avatar
1 vote
1 answer
151 views

Amplitude modulation in pure sine wave [duplicate]

I am generating sine wave in MATLAB with following code ...
user777304's user avatar
2 votes
2 answers
144 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/...
rhz's user avatar
  • 457
3 votes
1 answer
578 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 ...
JeffThompson's user avatar
0 votes
1 answer
128 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}...
usernumber's user avatar
0 votes
3 answers
311 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 ...
mark leeds's user avatar
  • 1,117
8 votes
1 answer
387 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). ...
Olli Niemitalo's user avatar
-1 votes
1 answer
415 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 <...
Goktug's user avatar
  • 117
0 votes
1 answer
796 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: ...
Duck's user avatar
  • 137
0 votes
2 answers
56 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\...
Qqwy's user avatar
  • 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) ...
Mr.Sh4nnon's user avatar
4 votes
1 answer
958 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} \...
Yannick's user avatar
  • 145
1 vote
2 answers
876 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 ...
Sama Assi's user avatar
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;...
Park's user avatar
  • 69
0 votes
1 answer
134 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.: $$v(t) =\widetilde{v_{dc}} + \sum_{n=1}^{\infty}\sin(\omega_nt+\phi_n)$$...
MarkoP's user avatar
  • 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 ...
curious's user avatar
  • 81
0 votes
1 answer
321 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 $\...
Schimay's user avatar
  • 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 ...
MisterH's user avatar
  • 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 ...
Skaveelicious's user avatar
0 votes
2 answers
110 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 ...
user22945's user avatar
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 ...
MisterH's user avatar
  • 317