EEEE2055: Discrete/Fast Fourier Transforms Flashcards
(9 cards)
Describe how the number of samples in a signal affects the time taken to perform a Discrete Fourier Transform (DFT).
- Time is proportional to number of samples squared
Explain why the number of samples in a signal affects the time taken to perform a Discrete Fourier Transform (DFT).
- Each frequency output sample related to every input time sample
- Causes algorithm to have two nested loops
- Calculations = time x frequency
Explain the advantage of a Fast Fourier Transform (FFT) over a DFT and give a quantitative example to illustrate.
- Time for FFT proportional to nlogn samples
- Computational benefit for problems with large sample numbers
- Example: tDFT_1 = 4X, tDFT_2 = 100X
tFFT_1 = 1.38Y tFFT_2 = 23Y
State how the choice of parameters of the DFT affect both the resolution and the maximum frequency of the discrete spectrum.
- tmax = N
State the parameters of a DFT
- tmax/trecord = Time over which movement taken
- Δt = Sampling Rate
- N = Number of samples
State the equations needed for an FFT question
- fo = 2fs
- fs = 1/Δt
- Number of time samples = Recording length/Δt
- Recording length = 1/Frequency resolution
- Δt = 1/2fmax
State how a discrete Fourier transform differs from a continuous Fourier
transform.
- discrete Fourier transform operates on sampled data (Input Time-Sampled and Output Frequency-Sampled)
State how the sampling frequency and total time recording length affects
the results of a discrete Fourier Transform.
- Recording length affects frequency resolution, minimum record length must be period of smallest frequency
- Sampling period affects maximum frequency, sampling frequency must be greater than 2x the maximum frequency
Explain how a Fast Fourier Transform differs from a standard Discrete Fourier Transform. Give an example where Fast Fourier Transform might be used.
- FFT is faster as able to process larger data sets in less time
- DFT n^2
- FFT nlog(n)
- Example: Determine frequency in oscilloscopes
