Digital Leaky Integrator (First order IIR digital LPF)

[awais107]

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

 

[FvM]

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.

 

[awais107]

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.

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.

 

[FvM]

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.

 

[awais107]

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.

 

[FvM]

See https://en.wikipedia.org/wiki/Low-pass_filter#Passive_electronic_realization