# Questions tagged [fourier]

The tag has no usage guidance.

271 questions
Filter by
Sorted by
Tagged with
2k views

### Time-differentiation property of Fourier transform for $\sin(\omega_0t)$ and $\cos(\omega_0t)$ [duplicate]

As I know, the Fourier transform has the below property which is called time-differentiation: $$\frac{dx(t)}{dt}\leftrightarrow j\omega X(j\omega)$$ and the Fourier transform of the cosine and the ...
905 views

### Trying to decompose a signal into sine waves whose wavelengths aren't restricted to 1/N times sample range?

I am trying to essentially do a Fourier transform - I want to fit some data with sine/cosine functions. At first I was trying to do this using FFT, but my problem is that the FFT algorithm doesn't ...
754 views

### Why can FFT only operate on images with specific properties?

Can FFT only operate on Grayscale images? If Yes, why? Can FFT only operate on images with dimensions of power of two? If Yes, why?
559 views

### Can use of Fourier transform be minimized completely with the help of Laplace and Z transform?

Fourier transform has different types like continuous Fourier transform (CFT), Discrete time Fourier transform (DTFT) and Discrete Fourier transform ( DFT). CFT can be used in case of continuous ...
2k views

569 views

### Real Time Goertzel Algorithm

Why is Goertzel Algorithm considered a block algorithm? Given that my input is bounded, couldn't I just run it forever (taking every sample that comes out after some length N) given a big enough word ...
2k views

### Power Spectral Density computation and units

I want to make some calculs of power spectral densité of signal. For example a real voltage signal (physical unit : $V$) in time $g(t)$, its fourier transform $G(f)$ and $S_g(f)$. As far as I know,...
2k views

### LTI system response to periodic input

I'm trying to find the zero-state response (ZSR) of an LTI system to a one sided periodic input, like a square wave that is equals to zero for $t < 0$. I know that I can use the Fourier series of ...
164 views

### Complex Conjugate Sinusoids in Forward DFT

I hope this isn't such a dumb question, but I'm finally getting to grips with the inner workings of the DFT. What I'm having trouble understanding is why the basis complex sinusoids in the "forward" ...
9k views

### Flat top sampling to a step shape signal

Flat Top Sampling During transmission, noise is introduced at top of the transmission pulse which can be easily removed if the pulse is in the form of flat top. Here, the top of the samples are flat i....
334 views

### Fourier Transform/Series DFT/DFS textbook problem (simple?)

Suppose $x_c(t)$ is a periodic continuous time signal with period 1 ms and for which the Fourier series is \begin{align*} x_c(t) &= \sum\limits_{k=-9}^9 a_k e^{j(2000 \pi k t)} \\ \end{align*} ...
2k views

### Inverse Fourier Transform problem

One of my tutorial questions for communication systems asks me to find the time function $x(t)$ which has the Continuous-Time Fourier Transform: $$X(\omega) = \frac{3}{(1+j\omega)(2-j\omega)}$$ So far ...
1k views

### What do colored noises look like in the time domain?

I understand that the time domain representation of white noise looks like impulses. How do colored noises like brown, pink etc. look like when we perform an inverse Fourier Transform on them ? What ...
258 views

### Fourier Transform of triangle function $x(t)=\Delta\left(\frac{t-1}{2}\right)$

Can you please tell me if my working is right for the Fourier Transform of this function: $$x(t)=\Delta\left(\frac{t-1}{2}\right)$$ My workings are: I have used the fourier transform standard ...
285 views

### Fourier transform 4 times = original function (2D and higher)

The Signal Processing SE post linked below shows how the Fourier Transform applied 4 times to a 1D function returns the original function, i.e. F{ F{ F{ F{ g(x) } } } } = g(x) Link to 1D case: ...
161 views

### Calculating original signal from Discerete Fourier Transform

I am trying to calculate the original equation using a DFT. I start with a equation, generate values from this equation and then get the dft of these values. The aim is to generate the original ...
424 views

### Fourier Transform of exponential

While solving Example 4.1 of Signals and Systems by Alan Oppenheim. Example 4.1 is: $$x(t)=e^{-at}u(t), a>0$$ and the transform I get is: $$X(j\omega)\frac{1}{a+j\omega}, a>0$$ The problem is ...
47 views

### Is there a way to go from a set of (F/D)FT values to FIR coefficients?

I'm not yet well educated on the DSP subject, but I've initiated a project where I will do some audio filtering. My intuition tells me that there is a link between the coefficients of a FIR filter and ...