Sampling Signals Part 2 (2/10) - Time-Bandwidth Product Matlab Script

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The previous video in this playlist introduced the time-duration (Td) and bandwidth metrics (Bw) and said that the time-bandwidth product was always greater than or equal to 1/2 (i.e Td*Bw greater than or equal to 0.5).

This video examines the this time-bandwidth product via experimenting with a Matlab script.  The continuous time-signal x(t) = exp(-a|t|) is parameterized by "a" which controls how quickly the signal decays in the time-domain.  The spectrum of this signal (i.e. X(w)) is computed analytically and both Td and Bw are computed numerically in Matlab.  We show that as "a" varies, the spectrum changes accordingly (compression in time leads to expansion in frequency and expansion in time leads to compression in frequency).  Also, regardless of the values of Td and Bw, we still have Td*Bw greater than or equal to 1/2 as expected.

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• #education
• #signal_time_bandwidth_product
• #time_bandwidth_product
• #signal_spectrum
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• #bandwidth
• #uncertainty_principle
• #time_frequency_duality
• #time_limited_signal
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• #matlab_signal_bandwidth
• #matlab_time_duration
• #time_limited_signals