`jwave.signal_processing`

`analytic_signal(x, axis=-1)`

Computes the analytic signal from a real signal x, using the FFT.

Parameters:

Name	Type	Description	Default
`x`	`jnp.ndarray`	[description]	required
`axis`	`int`	[description]. Defaults to -1.	`-1`

Returns:

Type	Description
`Array`	jnp.ndarray: [description]

`apply_ramp(signal, dt, center_freq, warmup_cycles=3)`

Processes the signal $s(t)$ as

$$ s(t)\cdot \text{min}(1, f_0t/\sigma) $$

Parameters:

Name	Type	Description	Default
`signal`	`jnp.ndarray`	[description]	required
`dt`	`float`	[description]	required
`center_freq`	`float`	$f_0$	required
`warmup_cycles`	`float`	$\sigma$. Defaults to 3.	`3`

Returns:

Type	Description
`Array`	jnp.ndarray: [description]

`blackman(N)`

Returns the blackman window of length N

Parameters:

Name	Type	Description	Default
`N`	`int`	[description]	required

Returns:

Type	Description
`Array`

`fourier_downsample(x, subsample=2, discard_last=True)`

Downsample a signal by taking the Fourier transform and discarding the high frequencies.

Parameters:

Name	Type	Description	Default
`x`	`jnp.ndarray`	Signal to be downsampled	required
`subsample`	`int`	Sumsampling factor. Defaults to 2.	`2`
`discard_last`	`bool`	If True, the last dimension is not subsampled. Defaults to True.	`True`

Returns:

Type	Description
`Array`	jnp.ndarray: [description]

`fourier_upsample(x, upsample=2, discard_last=True)`

Upsample a signal by taking the Fourier transform and adding zeros at the high frequencies.

Parameters:

Name	Type	Description	Default
`x`	`jnp.ndarray`	Signal to be upsampled	required
`upsample`	`int`	Upsampling factor. Defaults to 2.	`2`

Returns:

Type	Description
`Array`	jnp.ndarray: Upsampled signal

`gaussian_window(signal, time, mu, sigma)`

Returns the gaussian window

$$ s(t)\cdot \exp \left( - \frac{(t-\mu)^2}{\sigma^2} \right) $$

Parameters:

Name	Type	Description	Default
`signal`	`jnp.ndarray`	$s(t)$	required
`time`	`jnp.ndarray`	$t$	required
`mu`	`float`	$\mu$	required
`sigma`	`float`	$\sigma$	required

Returns:

Type	Description
`Array`	jnp.ndarray: [description]

`smooth(x, exponent=1.0)`

Smooths a n-dimensioanl signal by multiplying its spectrum by a blackman window.

Parameters:

Name	Type	Description	Default
`x`	`jnp.ndarray`	[description]	required

Returns:

Type	Description
`Array`	jnp.ndarray: [description]

`smoothing_filter(sample_input)`

Returns a smoothing filter based on the blackman window, which works on a signal similar to the one provided as input. The filter is amenable to jax transformations.

Parameters:

Name	Type	Description	Default
`sample_input`	`jnp.ndarray`	Example signal	required

Returns:

Name	Type	Description
`Callable`	`Callable`	Smoothing filter

`tone_burst(sample_freq, signal_freq, num_cycles)`

Returns a tone burst

Parameters:

Name	Type	Description	Default
`sample_freq`	`float`	Sampling frequency	required
`signal_freq`	`float`	Signal frequency	required
`num_cycles`	`float`	Number of cycles	required

Returns:

Type	Description
`Array`	jnp.ndarray: The tone burst signal