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Digital Leaky Integrator (First order IIR digital LPF)

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awais107

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Hi

I need some guidance regarding the implementation of Digital Leaky Integrator (First order IIR digital LPF) using full custom flow. I implemented the following:
https://www.physi.uni-heidelberg.de/~angelov/VHDL/VHDL_SS09_Teil06.pdf (slide 32)

Attached (Doc4.docx )

But the simulation in cadence take too much time and don't finish at all. I want to make a IIR digital LPF having cut-off frequency of 0.01Hz.

Awais
 

You should also pay attention to the rounding problem discussed in slide 37 and 38. For full output accuracy, the accumulator range must be increased according to the ratio fs/fc (sampling to filter cut-off frequency). Thus a 0.01 Hz filter should use a moderate sampling frequency. This reduces also simulation time.
 
FvM said:
You should also pay attention to the rounding problem discussed in slide 37 and 38. For full output accuracy, the accumulator range must be increased according to the ratio fs/fc (sampling to filter cut-off frequency). Thus a 0.01 Hz filter should use a moderate sampling frequency. This reduces also simulation time.
Click to expand...


Thanks. Also, one another thing. Normally in digital leaky integrator what is the settling time for lets say 0.01Hz cut-off frequency. As, in analogue implementation the settling time will be very high for the similar specifications.
 

For systematical clarity, we should name the design what it is, a first order digital low pass filter. "digital leaky integrator" is more a visual description of it's operation. I recognize that it's from a VHDL lecture for physicists.

With suffcient high fs/fc ratio, the time discrete behaviour of the digital filter is effectively identical with a time continuous filter. A first order filter with 0.01 Hz cut-off frequency has a time constant of 16 Hz and a respective exponential step response. Settling to 99 % takes e.g. 4.6 time constants, easy to calculate. Depending on your application, the "infinite" in IIR might be inconvenient and a FIR filter more suitable.
 
Can you elaborate how the cut-off frequency of 0.01Hz has time constant of 16Hz. If you can share the mathematical background regarding and how to calculate it.
 

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