The characteristics of various transformations in time domain and frequency domain
Fourier series (FS: Fourier series): time domain periodic continuous signal, frequency domain discrete aperiodic signal
Fourier transform (FT: Fourier transform): time domain aperiodic continuous signal, frequency domain continuous aperiodic signal
Discrete Time Fourier Transform (DTFT) : discrete time Fourier transform: discrete time domain aperiodic signal, frequency domain periodic continuous signal
Discrete Fourier transform (DFT: discrete Fourier transform): time domain discrete periodic signal, frequency domain periodic discrete signal
Knowledge points
1. Understand the definitions of continuous-time signals and discrete-time signals. Discrete-time signals are obtained by sampling the continuous-time signals at equal periods and expressed in discrete time series. Among them, the discrete time sequence x(n) is subjected to DTFT (Discrete Fourier Transform) to obtain the frequency domain signal, where w represents the digital angular frequency, pay attention to the difference with the analog angular frequency.
2. The necessary and sufficient condition for a stable system is that the impulse response is absolutely summable. The definition of a causal system: the output of the system is only related to the current input or the previous input, and has nothing to do with the subsequent input; therefore, the necessary and sufficient condition is h(n)=0, When n<0; pay attention to the difference between FIR system and IIR system: use the difference equation to express the system, FIR has no feedback, and IIR has feedback.
3. For discrete periodic sequences, DFS is performed to obtain frequency domain signals, where frequency domain signals are also periodic; for discrete non-periodic finite-length signals, DFT is performed to obtain frequency domain signals, which can be obtained by period extension to obtain a periodic sequence, which is understood as The main value interval of the DFS sequence.
4. The analog signal needs to be sampled and sent to the computer for processing. The sampled signal is different from a discrete time sequence. The sampled signal spectrum is a periodic shift of the original signal spectrum. The shift interval is the sampling frequency, and then the simulation is restored through an anti-aliasing low-pass filter The signal can be proved by formula derivation.