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Questions tagged [fourier-series]

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5 votes
1 answer
269 views

Compare two Fourier series to depict the signal smoothness

I have several signals, that I am trying to find a metric to compare the signal smoothness. By signal smoothness I mean, the signal that the distance between the peak to trough become smaller (getting ...
• 51
3 votes
0 answers
165 views

What happens to sidebands when they enter "negative" frequencies?

I am working with PWM signals. These signals are generated by comparing a modulating (at frequency $f_m$), and a carrier (at frequency $f_c$), as shown in the following image: In the resulting ...
• 125
3 votes
0 answers
221 views

Improving the intuition for the 2d fourier transform

As far as I understand, the 2d fourier transform is calculated as following: ...
• 131
2 votes
0 answers
2k views

Fourier series representation of a full wave rectifier output

I am trying to compute the Fourier series representation of a full wave rectifier output. The equation of the signal is: $x_8(t) = | \cos (2 \pi f_o t)$ | I have tried to find the Fourier series ...
• 361
2 votes
0 answers
66 views

Power contained in a signal

Given a signal $$x(t)=16\cos(20\pi t+\frac\pi 4)+6\cos(30\pi t+\frac\pi 6)+4\cos(40\pi t+\frac\pi 3)$$how can I calculate the power contained in a frequency interval, say 12Hz to 22Hz. The total power ...
• 169
2 votes
1 answer
470 views

Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away? Suppose we are given the ...
1 vote
0 answers
74 views

Finding $A_k$ coefficients

I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as: $x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
1 vote
0 answers
85 views

Pitch successfully changes with Phase Vocoder, but there's an issue

I've been working on a phase vocoder program. The goal is to change the pitch of a recording of my voice. While doing research on how to change pitch, I came across this from a paper on phase vocoders ...
1 vote
0 answers
118 views

What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?

$\DeclareMathOperator{\sinc}{sinc}$ I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem. Context When ...
1 vote
0 answers
126 views

• 111
1 vote
0 answers
32 views

Efficient format for 2D signal?

I'm trying to solve the following problem. I got a "low frequency" input 2D signal over a square region. I'll collect a few samples, somewhere around 10-30 maybe, the exact sample count will be ...
1 vote
0 answers
8k views

The Fourier Series, Amplitude and Phase Plot of a Saw Tooth Waveform

I am trying to find the amplitude and phase plots of the saw tooth waveform pictured.I have already computed the Fourier series of the waveform but I don't know how to derive the amplitude and phase ...
• 326
1 vote
0 answers
160 views

A Laymans Fourier transform and harmonics explanation?

Please bear with me, I know some of you will scoff but I have looked on Wiki and in various literature (see below) and can't quite get a handle on a few things. I am a general business programmer, ...
• 111
1 vote
1 answer
99 views

On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies

It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
0 votes
1 answer
185 views

Can someone explain me how the phase spectrum of trigonometric fourier series is related to phase spectrum of exponential fourier series of a signal?

Suppose we take a periodic signal and perform fourier analysis over it . Now we have two ways of representing the fourier series of this particular signal , one is trigonometric fourier series and ...
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0 votes
0 answers
40 views

Separating 'heart sound' from 'lung sound'

I have audio files recorded from electronic stethoscope and in those files I want to filter out heart sounds and retain just the breathing sounds. How can I do this using just the signal processing ...
0 votes
0 answers
26 views

Advantages of the Karplus algorithm for sound synthesis

For a personal project I am trying to make a software to synthesize plucked and hammered string instruments. This is a whole research topic and there are already some models and algorithms such as the ...
0 votes
0 answers
64 views

Finding the Fourier Coefficients

Up until now, I have dealt with finding Fourier Coefficients for functions: $f(t) > 0$ Which made it convenient calculating the Fourier Analysis Integral. However, I am now presented with ...
0 votes
0 answers
90 views

How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?

Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match. I am trying to generate a sound closer to a saxophone using ...
0 votes
0 answers
381 views

How do I plot a phase spectrum of rectangular pulse with Matlab?

As you can see, I made a code about rectangular pulse like this. And, I plotted complex-exponential-coefficient and Magnitude-Spectrum-of-Complex-Exponential-Form, Phase-Spectrum of-Complex-...
0 votes
0 answers
215 views

Approximation of Periodic Parabolic Function by Fourier Series!

I've just tried to approximate the periodic-parabolic signal by Fourier Series. I know, this sounds a bit strange. I am just trying to figure out relationship between Fourier Series and Taylor ...
0 votes
0 answers
21 views

Square pulse test of Upwind Finite Differences

I`m analyzing the numerical methods for the 1D convection equation for stability, consistency, and accuracy. I want to see How does this square pulse move in domain and time? Here is my code % ...
0 votes
0 answers
68 views

How to get coefficient of the discrete fourier Series from the fourier transform

Given $X(v)$ the Discrete Fourier transform of a discrete periodic signal $x(n)$, it's possible to arrive to the $c_k$ of the Fourier series $$x(n)=\sum_{k=0}^{n-1} c_k \exp(2\pi i k t)$$ directly?
0 votes
0 answers
222 views

Rectangular Pulse Train and Sinc Function

I wanted to ask that in frequency domain the rectangular pulse is a sinc function, so is this sinc function periodic or aperiodic? Also if signals that are continuous in time domain then they are ...
0 votes
0 answers
155 views

Can different Discrete-Time-Fourier-Series(DTFS) coefficients have the same discrete sequence in the time domain?

Please, check the following discrete periodic sequence when the period $N=2$. $x[k]=\exp(j\frac{2\pi}{N}k), N=\text{period}$ $..., x[0]= 1, x[1]= -1, x[2]= 1, x[3]= -1, ... , N=2$ According to my ...
0 votes
0 answers
33 views

Redundancy when using Nyquist rate for a time series

I sample temperature at one sample per second (the hardware I am using takes the temperature at this rate, so this is the max I can efficiently sample.) The Nyquist rate for this signal would be 2 ...
0 votes
0 answers
40 views

How to apply FT to real-life signal that labeled in seconds, not radians

In training examples we always do a transformation on signals which have t-scale in labeled in radians. I understand that Pi is just a number, but I still have some troubles to understanding how to ...
• 57
0 votes
0 answers
43 views

frequencies in frequency spectrum with no correlation together

I have a lack of understanding of the following questions: If I have a signal from a motor that is recorded with an accelerometer. And the rotating speed of the motor is 150Hz(rpm 9000 ), I can see in ...
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0 votes
0 answers
111 views

• 249
-1 votes
1 answer
109 views

Why do we scale bins in FFT in this code?

Hi I am learning FFT I am confused about this bit of code: what is the reason for scaling the sampling frequency and what is bin scale and why and when do we use it? thank you ...
-1 votes
1 answer
565 views

Fourier Coefficients

Consider the signal $$x(t)=\cos(2\pi t)$$ Since $x(t)$ is periodic with a fundamental period of $1$, it is also periodic with a period of $N$, where $N$ is any positive integer. What are the ...
-1 votes
1 answer
201 views

Fourier series qn determine the fourier series coefficients

Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of $x(t)$ given as $x(t) = > \cos4t +\sin8t+3$?
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