Properties
This table shows some mathematical operations in the time-domain and the corresponding effects in the frequency domain.
- is the discrete convolution of two sequences
- is the complex conjugate of
| Property | Time domain | Frequency domain | Remarks |
|---|---|---|---|
| Linearity | |||
| Shift in time | integer k | ||
| Shift in frequency (modulation) | real number a | ||
| Time reversal | |||
| Time conjugation | |||
| Time reversal & conjugation | |||
| Derivative in frequency | |||
| Integral in frequency | |||
| Convolve in time | |||
| Multiply in time | Periodic convolution | ||
| Cross correlation | |||
| Parseval's theorem |
Read more about this topic: Discrete-time Fourier Transform
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