Frequency Analysis

Question 1

Block Processing Trade-Off

Answer 1

Analysis of smaller blocks increases time resolution but decreases frequency resolution and vice versa

Question 2

Narrowband Frequency Analysis

Answer 2

• Increasing frame N (20-30ms) leads to NB analysis
• Decreases the spacing between the spectral components (good spectral resolution)
• Reduces the ability to respond to changes in the signal (poor time resolution)
• Useful for analysis of harmonics

Question 3

Wideband Frequency/Broadband Analysis

Answer 3

• Decreasing frame N (3-5ms) leads to WB analysis
• Increases the spacing between the spectral components (good time resolution)
• Increases the ability to respond to changes in the signal (poor spectral resolution)
• Useful for analysis of formants

Question 4

Frequency Resolution (through time T)

Answer 4

Δf = 1 / (NT)

Question 5

Z-Transform

Answer 5

Turns messy time-domain recursion into clean algebra.

Question 6

Transfer Function

Z-Transfers

Answer 6

H(z) = Y(z) / X(z)

Question 7

Time Shifting Z-Transform

Answer 7

Z{ x[k-k0] } = z^-k0 * Z{x[k]}

Question 8

Poles

Answer 8

• Roots of the denominator
• Frequencies at which a filter transfer function tends to infinity i.e. ʻresonancesʼ

Question 9

Zeros

Answer 9

• Roots of the numerator
• Frequencies at which a filter transfer function tends to zero i.e. ʻanti-resonancesʼ

Question 10

Geometric Series

Answer 10

sum (cr^k) = c / (1-r) for |r| < 1

Question 11

DFT vs FFT

Answer 11

• Implementation of the DFT requires the order of N^2 multiply-add operations
• FFT exploits symmetry to require only Nlog2N multiply-add operations

e.g. for N=2048, the result is ~100x faster

• The FFT requires that the window/frame should be a power of 2 in size