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Computational savings of polyphase interpolation/decimation

Assume that we design FIR LPF H z with N taps, requiring N multiplies per output. For standard decimation by factor M , we have N multiplies per intermediate sample and M intermediate samples per output, giving N M multiplies per output.

For polyphase decimation, we have N M multiplies per branch and M branches, giving a total of N multiplies per output. The assumption of N M multiplies per branch follows from the fact that h n is downsampled by M to create each polyphase filter. Thus, we conclude that thestandard implementation requires M times as many operations as its polyphase counterpart. (For decimation, we count multiplesper output, rather than per input, to avoid confusion, since only every M th input produces an output.)

From this result, it appears that the number of multiplications required by polyphase decimation isindependent of the decimation rate M . However, it should be remembered that the length N of the M -lowpass FIR filter H z will typically be proportional to M . This is suggested, e.g. , by the Kaiser FIR-length approximation formula N -10 10 logbase --> δ p δ s 13 2.324 Δ ω where Δ ω in the transition bandwidth in radians, and δ p and δ s are the passband and stopband ripple levels. Recall that, to preserve a fixed signal bandwidth, the transitionbandwidth Δ ω will be linearly proportional to the cutoff M , so that N will be linearly proportional to M . In summary, polyphase decimation by factor M requires N multiplies per output, where N is the filter length, and where N is linearly proportional to M .

Using similar arguments for polyphase interpolation, we could find essentially the same result. Polyphase interpolation byfactor L requires N multiplies per input, where N is the filter length, and where N is linearly proportional to the interpolation factor L . (For interpolation we count multiplies per input, rather thanper output, to avoid confusion, since M outputs are generated in parallel.)

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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what is inorganic
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Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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progressive wave
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Digital signal processing (ohio state ee700). OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10144/1.8
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