Some Weyl-Heisenberg frame bound calculations

Analyzing the Weyl-heisenberg Frame Identity

In 1990, Daubechies proved a fundamental identity for WeylHeisenberg systems which is now called the Weyl-Heisenberg Frame Identity. WH-Frame Identity: If g ∈ W (L∞, L), then for all continuous, compactly supported functions f we have: ∑ m,n | < f, EmbTnag > | = 1 b ∑

A Necessary Condition for Weyl-Heisenberg Frames

Roots of Complex Polynomials and Weyl-heisenberg Frame Sets

A Weyl-Heisenberg frame for L2(R) is a frame consisting of modulates Embg(t) = e 2πimbtg(t) and translates Tnag(t) = g(t − na), m,n ∈ Z, of a fixed function g ∈ L2(R), for a, b ∈ R. A fundamental question is to explicitly represent the families (g, a, b) so that (EmbTnag)m,n∈Z is a frame for L2(R). We will show an interesting connection between this question and a classical problem of Littlewoo...

Some counterexamples in the theory of Weyl-Heisenberg frames

g Z I Y ( t ) = exp (-nizy + 27r iy t ) g ( t z), t E w We truncate the channel response so that N , = 0 and AT, = 20. As before, the channel input is an i.i.d. sequence, and the noise is stationary and white with SNR,h,, =20 dB. We assume the number of feedforward taps is fixed at q = 10. Fig. 3 shows the optimal decision delay (defined as thlat which maximizes SNRDFE) versus the number of fee...

Discrete Weyl–Heisenberg transforms

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