Recall Sampling

Sampling: process of taking a sample (value) of a continuous waveform at regular time intervals $T_s$.

Sampling rate: frequency at which samples are taken:

$$f_s = \frac{1}{T_s}$$    Hz$$.$$

Sampling the continuous-time sinusoid:

$$x(t) = A\sin(\omega t + \phi),$$

involves substituting continuous-time $t$ with integer $n$ multiples of the sampling period $T_s$:

$$t \longrightarrow nT_s$$

yielding a discrete-time sinusoid:

$$x(n) = A\sin(\omega nT_s + \phi).$$

Integer $n$ corresponds to the index of sequence $x(n)$.

Sinusoid $x(n)$ may be implemented as an array or wavetable.