# Questions tagged [fourier]

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### y(t) a of an integrator circuit

I have a signal $$x(t)= \frac{1}{T} e^{-\frac{t}{T}} u(t) - \frac{1}{T} e^{\frac{t}{T}} u(-t)$$ and I know that it transits in a integrator circuit and I have to find y(t) in time and frequency ...
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### Filtering Passband Signals using Complex Baseband Filtering

So I'm given a pass band filter with specific transfer function $H_p(f)$, I want to implement this via baseband processing. I already know how to take the input signal $u(t)$ and process it such ...
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### Regarding Bode plots; $H(s)$ and $H(j\omega)$

In circuit analysis, I understand the use of Laplace Transforms to obtain the impedance of a linear RLC circuit, ie transforming from the time domain to the frequency domain. In most texts I have seen ...
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### Energy of a sinc signal

My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me $$x(t)=\operatorname{sinc}(t)$$ and $$s(t)=x(t-T)$$ and I found that ...
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### Fourier transform properties

I have to find the Fourier transform of $$x(t)= \frac{1}{T}e^{-\frac{t-T}{T}}u(t-T)$$ First I applied traslation property , so $$F[x(t-T)] = X(f) e^{-i 2 \pi f T}$$ after I applied time scaling ...
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### Finite sequence input to DTFT

i'm studying the practical utility of Fourier transforms and i have some questions. I hope to receive answers in layman terms. 1) Does the DTFT take only infinite input sequences? 2) If i apply the ...
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### Fourier coefficients of 1/(1+it)

I have to find the Fourier coefficients of $$\frac{1}{1+ t^{2}}$$ I tried with $$\frac{1}{T}\int_{0}^{T} \frac{1}{1+it}e^{-i 2 \pi f_0 T }$$ but I should do at least two integrals by parts , so I ...
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### Fourier coefficients of odd and even part of a signal

I have this signal and I have to find the Fourier coefficients of the odd and even part. First I found that $$x_p(t) = \frac{1}{2} ( x(t) + x(-t) )$$ and I made the graphic of this part and I ...
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### E of a signal using Rayleigh

I have to find The energy of a signal using Rayleigh th. the signal is $$x(t) = A e^{-At } u(t)$$ assuming A>0 Using the classic definition of E , I found that it should be $$\frac{A}{2}$$ Using ...
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### Why does DTFT start and end at the same magnitude?

I would like to know why the spectrum of FIR filters (and maybe all DTFT spectra) start and end at the same magnitude. I guess there is something related to $H(e^{j\omega})$. Thanks
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### Amplitude of an Image

If I take a two dimensional image and conduct a fourier transform on it, I would get a two dimensional matrix of complex values. If I want to find the amplitude of each value, is that the same as ...
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### What determines peaks in FFT?

I ran FFT on three audio files and found that the results for some have more peaks than the other. Could anyone give me any conceptual explanation as to what determines these peaks? Below are plots of ...
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### What is Imaginary in Fourier transform?

How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
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### Impulse response of a 3x3 PSF - how to find analytical expression for fourier transform of a 3x3 matrix?

I have a filter $\mu[n_1, n_2]$ with taps: $$(1/8) (1/4) (1/8)$$ $$(1/4) (1/2) (1/4)$$ $$(1/8) (1/4) (1/8)$$ How do I find an analytical expression for $\hat\mu(w_1, w_2)$? Since it looks so ...
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### Range Doppler Maps

I would like to understand from a high point of view how these maps are computed. On the y-axis we have m/s and in the x-axis the range. I read something about the Fourier transform etc, but I don't ...
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### Is it correct to assume that $(-1)^n = \cos(\pi n)$ while computing the DTFT of $(-1)^n$?

$\cos(\pi n)$ fluctuates between $-1$ and $1$ depending on the values of $n$, and it would be the same as computing it with an exponential but the problem is that I just get part of the right answer......
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### When plotting the cosines of the phases of some sensors, I got an interesting plot

I have a laser that I modulate at some frequency, typically 1250 Hz. I have a sensor that tracks what happens inside a reactor when it's illuminated. I am doing Fourier analysis on both the laser ...
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### DFT truncation of signals

How can I calculate 8 point DFT of signals whose length is less then 8 ( say 2,4) then what will I assume other members in formulae "0" or rotation or keep repeating the same two numbers Consider I ...
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### How do I obtain the fourier series coefficients for a signal obtained by multiplication of two signals of different frequency?

What i assume here is that LCM of time periods of the two taken signals exist that is signals periods are not like pi/2 and 1 but are rather like 1 and 2 (just an example) I am given fourier series ...
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### What happens if I zero out the initial terms of the fft output and take inverse fft? [duplicate]

I am new to signal processing domain. When I run fft on data of length 1000, I get 1000 complex numbers. Now, if I want to extract the low frequency information or signal approximation, I take the ...
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### DFT: a function of $n$?

I‘m a high school student and I haven’t studied physics or anything. Why does the DFT depend on an integer, say $k$ or $n$ (it’s usually expressed like $F(n)=...$ or $F(k)$ or $F_k$, etc.) if it is ...
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### How to get descrete fourier tarnsfom [closed]

Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
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### How would I find the function given the magnitude plot and the phase response?

I'm wondering how I'd find the Fourier Transform X(jw) given the following information: My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
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### Filtering out different narrow-band frequencies at once

I have asked a closely related question on SO at https://stackoverflow.com/questions/55168460/python-implementation-for-filtering-out-multiple-distinct-narrow-band-frequencie but I am still unclear ...
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### Help me understand the stages involved in filtering a signal using Discrete Fourier Transform

I have a series of discrete values measured from a sensor. I want to filter the frequencies coming from this sequence of values. Then, if I understood the process correctly this is what I do: I ...
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### Fourier decomposition in Matlab

I am doing a Fourier decomposition of sea level series ( to find out one particular contribution within the sea level height). it should be applied subsequently on shifted (by one hour) windows of 96 ...
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### Detrend data with no clear secular trend prior to Fourier analysis?

I am completing Fourier analysis on many different time series of sediment particle flux exiting an experimental flume. Data is collected at a resolution of 1 Hz for durations ranging from ~5,000 to ...
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### What is the basic idea behind Fourier transform? [closed]

What is the basic idea behind (discrete and continuous) Fourier transform (FT)? In short, what is the difference between discrete and continuous FT? I have read multiple answers on the web related to ...
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### Fourier Transform minimum sample requirement

Assuming a signal is sampled adequately, what is the minimum size of an FFT window that would allow detecting a specific frequency? Is it necessary to have samples for at least one complete period at ...
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### Discrete Harmonics - Why multiplying digital frequency by k does not get next harmonic

For continuous time $e^{jk\Omega_0t}$ gives a complete set of orthogonal harmonics for fourier decomposition but for discrete $e^{jk\omega_0n}$ does not form a complete set orthogonal basis set ...
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### Linearity with Difference Period in Fourier Transform

I know that a system is linear if it satisfies $$\mathscr{F}\{ a\,x(t)+b\,y(t) \} = a\,X(\omega)+b\,Y(\omega)$$ for Fourier transform, $X(\omega)\triangleq\mathscr{F}\{x(t)\}$ But what if $x(t)$ ...
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### Does the Fourier series coefficient of AC components remains same if DC component is subtracted form the given signal?

Suppose a signal is defined by $x(t)= \begin{cases} t & 0\leq t \leq 1 \\ 2-t & 1\leq t\leq 2 \\ \end{cases}$ Since $x(t)$ has even symmetry, I can calculate fourier coefficient as  a_n = ...
If i take the Fast Fourier Transform (FFT) of a cosine function, what has turned this cosine function into its complex exponential form which consists of $e^{i \omega t} + e^{-i \omega t}$ ? Because ...