I have understood idea of discrete time and continuous time but I am feeling difficult to comprehend this idea in regard to frequency.

As for example the DFT output is discrete and the DTFT output is continuous.

How we can realize/visualize difference between continuous frequency and discrete frequency?

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    $\begingroup$ I’m voting to close this question because "discrete" is a term, as already explained by others in a previous answer, that simply applies to anything quantifiable. There's no difference between frequency, time, voltage, height, weight, amount of water... We're not a dictionary copied out on demand. $\endgroup$ – Marcus Müller Jun 14 '20 at 16:40
  • $\begingroup$ Previous question / answer: dsp.stackexchange.com/questions/67911/… $\endgroup$ – Marcus Müller Jun 14 '20 at 16:40
  • $\begingroup$ Also, here's a question regarding the meaning of the word "discrete" posted by your classmate engr: dsp.stackexchange.com/questions/66691/… I'd generally recommend searching his questions for an answer to your questions first, since you tend to have very similar questions, and it's better to build upon questions that were already asked and answered than ask the same thing again! $\endgroup$ – Marcus Müller Jun 14 '20 at 16:47
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    $\begingroup$ If the OP has understood the ideas of discrete time and continuous time, I would be glad he/she provides an explanation :-). Maybe the questions could be rephrased to include some idea of practical computability? $\endgroup$ – Laurent Duval Jun 14 '20 at 16:50
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    $\begingroup$ Are you sure you do not want to ask about difference in the concept of frequencies of Discrete-time Sinusoids and Continuous-time sinusoids ? Because DFT Frequencies are discrete because $k$ in $\omega=\frac{2\pi k}{N}$ can take only integers from $0,1,2,...,N-1$ and DTFT frequencies can take any value on real line, so they are continuous frequencies. I somehow feel, when we initially learn discrete-time Sinusoids and the fact that they are not necessarily Periodic always, that might be a confusing concept. $\endgroup$ – DSP Rookie Jun 14 '20 at 21:11

Both continuous-time and discrete-time signals generally have a continuous spectrum. Only periodic signal have a discrete spectrum. You might be familiar with the Fourier series, which is just a frequency-discrete representation of a periodic signal. There is also a Fourier series representation of discrete-time periodic signals, which is of course also discrete in frequency.

The discrete Fourier transform (DFT) is basically a Fourier series representation of a finite length discrete-time signal, which is thought of as periodically continued outside its support. The actual spectrum of the finite-length signal is continuous in frequency, and the DFT computes equidistant samples of this frequency-continuous spectrum.

The DFT can be used to compute discrete approximations to the continuous-time as well as the discrete-time Fourier transforms, both of which are continuous in frequency. The DFT is used so frequently, because we have efficient algorithms for its computation. These algorithms are called Fast Fourier Transform (FFT) algorithms.

  • $\begingroup$ As far as i am able to understand your answer, frequency spectrum is discrete for periodic signals?whether continuous time periodic or discrete time periodic? $\endgroup$ – Man Jun 15 '20 at 6:00
  • $\begingroup$ @Man: That's right. $\endgroup$ – Matt L. Jun 15 '20 at 6:43
  • $\begingroup$ And then DFT should be periodic ?for discrete frequency $\endgroup$ – Man Jun 15 '20 at 12:02

The difference btx DTFT and DFT is the frequency value at which it is being evaluated.

The DTFT is being evaled at any given f, while the DFT is only being evaled at specific frequencies.

But I think an important nature of DTFT is highlighted when you try to evaluate a given sampled signal at impractical frequencies. Like low frequencies for short signals or frequencies higher than Nyquist. Doesn't work.


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