DSP Mathematical Notation Reference¶
Schema Version: 1.0.0
Signal Notation¶
Discrete Time Signals¶
| Symbol | Description | LaTeX | Unit |
|---|---|---|---|
x[n] |
Input signal at sample n | x[n] |
- |
y[n] |
Output signal at sample n | y[n] |
- |
h[n] |
Impulse response at sample n | h[n] |
- |
n |
Sample index (integer) | n |
- |
fs |
Sample rate (Hz) | f_s |
Hz |
T |
Sampling period (seconds) | T |
s |
Frequency Domain¶
| Symbol | Description | LaTeX |
|---|---|---|
X(ω) |
Fourier transform of x | X(\omega) |
X(f) |
Spectrum in Hz | X(f) |
H(jω) |
Frequency response | H(j\omega) |
|H(ω)| |
Magnitude response | |H(\omega)| |
∠H(ω) |
Phase response | \angle H(\omega) |
Parameters¶
Filter Parameters¶
| Symbol | Description | LaTeX | Range |
|---|---|---|---|
fc |
Cutoff frequency (Hz) | f_c |
[20, 20000] |
ω0 |
Normalized angular frequency | \omega_0 |
- |
Q |
Quality factor | Q |
[0.5, 20] |
G |
Gain (dB or linear) | G |
- |
BW |
Bandwidth | BW |
- |