Signal sampling and reconstruction below the nyquist rate

An apparatus for reconstructing an input signal, the apparatus comprising:

• a first sampler to sample an input signal at a sampling rate fs to provide a first sampled signal, the sampling rate being less than a Nyquist sampling rate for the input signal;
• a delay device to provide a delayed input signal;
• a second sampler to sample the delayed input signal at the sampling rate to provide a delayed second sampled signal;
• a first Fourier transform device responsive to the first sampled signal to provide a first signal spectral component;
• a second Fourier transform device responsive to the delayed second sampled signal to provide a second signal spectral component;
• and
• a de-aliasing device to combine the first signal spectral component and the second signal spectral component to provide a first de-aliased spectral component and a second de-aliased spectral component.

A method of processing an input signal, the method comprising:

• providing a first sampled signal by sampling an input signal at a sampling rate fs, the sampling rate being less than a Nyquist sampling rate for the input signal;
• providing a delayed input signal by delaying the input signal by a delay time;
• sampling the delayed input signal at the sampling rate to provide a second sampled signal;
• performing a Fourier transform of the first sampled signal to provide a first signal spectral component;
• performing a Fourier transform of the second sampled signal to provide a second signal spectral component;
• combining the first signal spectral component and the second signal spectral component to provide a first de-aliased spectral component and a second de-aliased spectral component;
• and
• performing an inverse Fourier Transform on the first de-aliased spectral component and the second de-aliased spectral component to provide a reconstructed signal.