Create a convolution kernel representing the sinc function.
Use this kernel to eliminate frequencies above a certain cutoff.
- Parameters
cutoff_frequency (float or Tensor) – Upper limit \(\omega_c\) of the range of frequencies that you want
to preserve. The filter eliminates components of the signal that have
higher frequencies.
- Returns
A node representing the sinc function to use in a convolution.
- Return type
ConvolutionKernel
Notes
The range of frequencies that this kernel lets pass is
\([-\omega_c, \omega_c]\). After a Fourier transform to convert from
frequency domain to time domain, this becomes:
\[\frac{1}{2\pi} \int_{-\omega_c}^{\omega_c} \mathrm{d}\omega
e^{i \omega t} = \frac{\sin(\omega_c t)}{\pi t}.\]
The function on the right side of the equation is the sinc function.
Its integral is the sine integral function (Si).
For more information on Stf nodes see the Working with time-dependent functions in
Boulder Opal topic.
Examples
Filter a signal by convolving it with a sinc kernel.
>>> sinc_kernel = graph.sinc_convolution_kernel(cutoff_frequency=300e6)
>>> sinc_kernel
<ConvolutionKernel: operation_name="sinc_convolution_kernel">
>>> pwc_signal
<Pwc: name="pwc_signal_#1", operation_name="pwc_signal", value_shape=(), batch_shape=()>
>>> filtered_signal = graph.convolve_pwc(pwc=pwc_signal, kernel=sinc_kernel)
>>> filtered_signal
<Stf: operation_name="convolve_pwc", value_shape=(), batch_shape=()>
Refer to the How to create leakage-robust single-qubit gates
user guide to find the example in context.