class sdr.Differentiator(sdr.FIR)

Implements a differentiator FIR filter.

Notes

A discrete-time differentiator is a FIR filter with the transfer function

\[H(z) = 1 - z^{-1} .\]

FIR Differentiator Block Diagram
x[n] --+---------------@--> y[n]
       |               ^
       |   +------+    | -1
       +-->| z^-1 |----+
           +------+

Examples

Create a differentiator FIR filter.

In [1]: fir = sdr.Differentiator()

Differentiate a Gaussian pulse.

In [2]: x = sdr.gaussian(0.3, 5, 10); \
   ...: y = fir(x)
   ...: 

In [3]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.time_domain(x, label="Input"); \
   ...: sdr.plot.time_domain(y, offset=-fir.delay, label="Derivative"); \
   ...: plt.title("Discrete-time differentiation of a Gaussian pulse"); \
   ...: plt.tight_layout();
   ...:
../../_images/sdr_Differentiator_1.png

Differentiate a raised cosine pulse.

In [4]: x = sdr.root_raised_cosine(0.1, 8, 10); \
   ...: y = fir(x)
   ...: 

In [5]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.time_domain(x, label="Input"); \
   ...: sdr.plot.time_domain(y, offset=-fir.delay, label="Derivative"); \
   ...: plt.title("Discrete-time differentiation of a raised cosine pulse"); \
   ...: plt.tight_layout();
   ...:
../../_images/sdr_Differentiator_2.png

Plot the frequency response.

In [6]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.magnitude_response(fir);
   ...:
../../_images/sdr_Differentiator_3.png

Constructors

Differentiator(streaming: bool = False)

Creates a differentiator FIR filter.

Special methods

__call__(x: ArrayLike, ...) → NDArray

Filters the input signal \(x[n]\) with the FIR filter.

__len__() → int

Returns the filter length \(N + 1\).

String representation

__repr__() → str

Returns a code-styled string representation of the object.

__str__() → str

Returns a human-readable string representation of the object.

Streaming mode only

reset()

Resets the filter state. Only useful when using streaming mode.

flush() → NDArray

Flushes the filter state by passing zeros through the filter. Only useful when using streaming mode.

property streaming : bool

Indicates whether the filter is in streaming mode.

property state : NDArray

The filter state consisting of the previous \(N\) inputs.

Methods

impulse_response(N: int | None = None) → NDArray

Returns the impulse response \(h[n]\) of the FIR filter. The impulse response \(h[n]\) is the filter output when the input is an impulse \(\delta[n]\).

step_response(N: int | None = None) → NDArray

Returns the step response \(s[n]\) of the FIR filter. The step response \(s[n]\) is the filter output when the input is a unit step \(u[n]\).

frequency_response(...) → tuple[NDArray, NDArray]

Returns the frequency response \(H(\omega)\) of the FIR filter.

frequency_response_log(...) → tuple[NDArray, NDArray]

Returns the frequency response \(H(\omega)\) of the FIR filter on a logarithmic frequency axis.

Properties

property taps : NDArray

The feedforward taps \(h_i\) for \(i = 0,...,N\).

property order : int

The order of the FIR filter \(N\).

property delay : int

The delay of the FIR filter \(d = \lfloor \frac{N + 1}{2} \rfloor\) in samples.