DigitalFilters

DigitalFilters - Basics of Digital Filters Elena Punskaya

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1 Basics of Digital Filters Elena Punskaya www-sigproc.eng.cam.ac.uk/~op205 Some material adapted from courses by Prof. Simon Godsill, Dr. Arnaud Doucet, Dr. Malcolm Macleod and Prof. Peter Rayner
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2 Digital Filter: numerical procedure or algorithm that transforms a given sequence of numbers into a second sequence that has some more desirable properties . What is a Digital Filter? Digital Filter Input sequence Output sequence x n y n
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3 Desired features Desired features depend on the application, for example Input Signal Output generated by sensing device (microphone) having less noise or interferences speech with reduced redundancy for more efficient transmission
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4 Examples of filtering operations • received radio signals • signals received by image sensors (TV, infrared imaging devices) • electrical signals measured from human body (brain heart, neurological signals) • signals recorded on analog media such as analog magnetic tapes Noise suppression
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5 Examples of filtering operations treble and bass control or graphic equalizers increase sound level and high and low level frequencies to compensate for the lower sensitivity of the ear at those frequencies or for special sound effects enhancement of edges in images improve recognition of object (by human or computer) edge – a sharp transition in the image brightness, sharp transitions in a signal (from Fourier theory) appear as high-frequency components which can be amplified Enhancement of selected frequency ranges
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6 Examples of filtering operations means of aliasing prevention in sampling communication radio or TV signal transmitted over specific channel has to have a limited bandwidth to prevent interference with neighbouring channels frequency components outside the permitted band are attenuated below a specific power level Bandwidth limiting
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7 differentiation integration Hilbert transform Specific operations Examples of filtering operations These operations can be approximated by digital filters operating on the sampled input signal
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8 Linear time-invariant (LTI) digital filters. We limit ourselves to LTI digital filters only. Time-invariant: Linear : defined by the principle of linear superposition LTI x n 1 y n 1 x n 2 y n 2 a 1 x n 1 + a 2 x n 2 a 1 y n 1 + a 2 y n 2 scaling & additivity properties x n - k y n - k If linear system's parameters are constant it is Linear Time Invariant x n y n
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9 Analysis • their time-domain characteristics – linear difference equations – filter’s unit-sample (impulse) response • their frequency-domain characteristics – more general, Z-transform domain • system transfer function • poles and zeros diagram in the z-plane – Fourier domain • frequency response • spectrum of the signal We analyse DSP algorithms by determining:
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