Upsampled input to an Adaptive filter?

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SUMMARY

The discussion centers on the implementation of the Least Mean Squares (LMS) adaptive filter in MATLAB, specifically addressing issues encountered when upsampling and low-pass filtering input signals. The user generates Gaussian noise using the "randn" function and observes that the estimated weight vector should represent a delta channel but instead resembles an "Sinc" function after upsampling. The conversation highlights the importance of understanding signal bandwidth and the cutoff frequency of the low-pass filter (LPF) used in the process.

PREREQUISITES
  • Understanding of Least Mean Squares (LMS) adaptive filtering
  • Familiarity with MATLAB programming and functions such as "randn"
  • Knowledge of signal processing concepts including upsampling and low-pass filtering
  • Basic principles of system identification in signal processing
NEXT STEPS
  • Research the impact of upsampling on adaptive filter performance
  • Learn about the design and implementation of low-pass filters in MATLAB
  • Explore the concept of signal bandwidth and its relevance to filtering
  • Investigate alternative adaptive filtering techniques beyond LMS
USEFUL FOR

This discussion is beneficial for signal processing engineers, MATLAB users, and researchers involved in adaptive filtering and system identification who seek to understand the effects of signal manipulation on filter performance.

khurram usman
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I will try to explain the issue I am having as clearly as possible without going into my coding or maths. I have my own and a MATLAB Central implementation pf standard LMS in MATLAB. Fixed step size. No normalization or other stuff.

I am trying to use it in a system identification setup. I generate a vector of gaussian numbers using "randn" and give the same vector as input and desired response to the LMS filter. Now the estimated weight vector at the end should be a "delta" channel and this is what I get. Then i tried upsampling and interpolating the input vector by an integer number and repeating the same thing. This time around the estimated channel is of the shape of an "Sinc". I gave the interpolated signal as the input and the desired response as before. No changes.

Then i also tried low pass filtering the input vector and repeating the same thing. Again a "Sinc". Has anyone observed this before or know something about this? Please point out my mistake. Any suggestions or a discussion is also welcome.
 
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