PROBLEM 2:

LINEAR PREDICTION

The goal of this assignment is to teach you the fundamentals of parametric spectral estimation. We will focus on the technique known as linear prediction (LP).

• Generate a signal that consists of one sinewave of amplitude 5,000 and duration one second using a sample frequency of 8 kHz, and write it to an Sof file as a VectorFloat.
  
  
• Read the signal from this file into a VectorFloat, and compute a Fourier Transform on a 30 msec window centered at 0.5 secs. Plot the magnitude spectrum on a dB scale.
  
  
• Compute a linear predictive model using an order 1, 2, and 4. Plot the spectrum of the gain-matched LP model over the magnitude spectrum previously generated.
  
  
• Repeat the previous steps for a sum of sinewaves using frequencies of 500 Hz, 1000 Hz, and 1500 Hz, and amplitudes of 1,000, 5,000, and 1,000 respectively. Use orders of 2, 4, 6, and 8.
  
  
• Repeat the previous steps for a typical vowel excised from the middle of an word in the OGI Alphadigit corpus. Use orders of 4, 8, and 12.
  
  
• Repeat the previous step for a typical consonant excised from the OGI Alphadigit Corpus. Use orders of 4, 8, and 12. What do you observe about the relationship between the LP order and the type of sound?
  
  
• Repeat the previous step for a typical vowel excised from the SWB Corpus. Use orders of 1, 8, 12, and 22. What aspects of the spectrum does the first LP coefficient model? What do you observe about the impact of telephone-bandwidth speech on the ability of the LP model to match the spectrum?
  
  
• Repeat the previous step for "preemphasized" speech (process the speech through a first-order preemphasis filter). Also add a Hamming window to the analysis. What is the impact of this on the LP model?

Other interesting experiments that can be run include investigating how the spectral estimation accuracy varies with the frequency and phase of a sinewave, or generating data using an LP model (white noise processed through the all-zero filter) and determining if an LP analysis correctly identifies the coefficients. The latter problem is what got me interested in speech recognition. The former problem is something I investigated for my thesis.