Understanding Analytic Signal and Hilbert Transform

Key focus of this article: Understand the relationship between analytic signal, Hilbert transform and FFT. Hands-on demonstration using Python and Matlab. Introduction Fourier Transform of a real-valued signal is complex-symmetric. It implies that the content at negative frequencies are redundant with respect to the positive frequencies. In their works, Gabor [1] and Ville [2], aimed … Read more

Sampling Theorem – Bandpass or Intermediate or Under Sampling

Prerequisite: Sampling theorem – baseband sampling Intermediate Sampling or Under-Sampling A signal is a bandpass signal if we can fit all its frequency content inside a bandwidth . Bandwidth is simply the difference between the lowest and the highest frequency present in the signal. “In order for a faithful reproduction and reconstruction of a bandpass … Read more

Sampling Theorem – Baseband Sampling

For Matlab demo of sampling see here. “Nyquist-Shannon Sampling Theorem” is the fundamental base over which all the digital processing techniques are built. Processing a signal in digital domain gives several advantages (like immunity to temperature drift, accuracy, predictability, ease of design, ease of implementation etc..,) over analog domain processing. Analog to Digital conversion: In … Read more