# Questions tagged [fourier-series]

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### I want to understand the fundamental difference/connection between DFS, DFT and DTFT

I'm an EE student and I seem to miss some basic concept of my Signals course. We have learned about all the different Fourier methods available, but I don't seem to find a difference/understand it. As ...
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1 vote
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### Don't we need both negative and positive discrete complex exponentials to make a real discrete time signal?

For a continuous time periodic signal , the Fourier spectrum has both negative and positive complex exponentials in equal numbers ,but I have seen for some discrete time periodic signals it is not the ...
33 views

### why we don't get equal number of negative and positive complex exponentials for the DTFS of a discrete time periodic signal?

When we compute the Discrete time Fourier series of a discrete time periodic signal , why don't we get the same number of negative complex exponentials and positive complex exponentials ? Even though ...
1 vote
85 views

49 views

### positivity of the spectrum of quasi-stationary signals

I am working on the "System identification : theory for the user" by Lennart Ljung (freely available here) and it is one of these books which contains exercises but no answers... My exercise ...
• 507
530 views

### Trying to understand how to get this basic Fourier Series

I'm sorry if this kind of question isn't allowed, but I'm starting to learn Fourier series and I'm still not entirely sure what's going on... in this specific case, I'm trying to find the Continuous ...
1 vote
52 views

1 vote
80 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 ...
127 views

### Fourier coefficients of two discrete-time signals of different periods

I'm trying to understand the Fourier series coefficients of the sum of two discrete-time periodic signals. Consider two discrete-time periodic signals $x[n]$ and $y[n]$. $x[n]$ has period $N$, its ...
• 75
82 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 ...
187 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 ...
• 135
126 views

### Bandwidth of cosine of bandlimited signal

I have a signal $x(t)$ with bandwidth $B_x$, and I am taking its cosine to create $y(t) = cos(x(t))$. After checking the spectrum with FFT, it seems that $y(t)$ is also bandlimited. But, is there a ...
• 135
101 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 ...
563 views

### How to reconstruct original signal using IFFT after cutting past Nyquist limit

I'm working on a pitch shifting program. Everything works up to the point where I try to do the IDFT. Because I cut the DFT array past the Nyquist limit, when I run the IDFT, I don't get the same ...
1 vote
99 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 ...
366 views

### How to change fundamental frequency with DFT?

I'm working on a voice changer. My plan is to make it so that it can change your voice in various different ways, but right now I'm just trying to make it change your voice to "chipmunk voice&...
636 views

### How to Find "pitch" from Fourier Series

The end goal of my project is to create an autotune program, But the problem I'm trying to solve right now concerns finding the pitch of someone singing a note. I have written some code that performs ...
1k views

### Fourier transform of periodic functions

The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...