Signal analysing and synthesizing filter bank system

• US 4,799,179 A
• Filed: 01/27/1986
• Issued: 01/17/1989
• Est. Priority Date: 02/01/1985
• Status: Expired due to Fees

• Current Assignee: Telecommunications Radioelectriques et Telephoniques TRT
• Original Assignee: Telecommunications Radioelectriques et Telephoniques TRT
• Inventors: Masson, Jacques L. R., Picel, Zdenek
• Primary Examiner(s): Harkcom, Gary V.
• Assistant Examiner(s): Mai, Tan V.
• Application Number:
  US06/822,503
• Time in Patent Office: 1,086 Days
• Field of Search: 364/724
• US Class Current: 708/313
• CPC Class Codes: H03H 17/0266 Filter banks

Abstract

In a signal analysing and synthesizing filter bank system, the analysing bank receives a signal sampled at the rate f_e and produces N contiguous subbank signals sampled at the rate f_e /N. From the subband signals the synthesizing bank must recover the incoming signal. These filter banks are formed by modulation of a prototype filter by sinusoidal signals which, for subband k (O≦k≦N=1), have a frequency (2k30 1)f_e /(4N) and respective phases +(2k+1)π/4 and -(2k+1)π/4 for the analysing and synthesizing banks. These signals are furthermore delayed by a time delay (N_c -1)/2f_e), where N_c is the number of coefficients of the prototype filter. Preferably, the analysing bank is realized by the cascade arrangement of an N-branch polyphase network (12) and a double-odd discrete cosine transform calculating arrangement (14) and the synthesizing bank is realized by the cascade arrangement of a double-odd discrete cosine transform calculating arrangement (15) and an N-branch polyphase network (17).

Claims

1. A digital signal processing system comprising:

a. an analysing filter bank for dividing an incoming signal, sampled at a rate f₃ and occupying a frequency band limited to f_e /2, into N contiguous subband signals having respective bandwidths of f_e /2N and which are sampled at a rate f_e /N, said analyzing filter bank comprising N prototype low-pass filters, one for each subband and arranged in parallel along N respective branches, each prototype filter;

i. having a same finite and symmetrical impulse response;

ii. having a beginning-of-attenuation-band frequency f_a less than f_e /2N; and

iii. satisfying the condition H² (f)+H² (f_e /2N-f)=1 in a band of frequencies f extending from 0 to f_a, where H(f) is the absolute value of the frequency response to each prototype filter; and

iv. comprising a modulation input for receiving a modulation signal, each modulation signal having;

A. a frequency f_k =(2k+1)f_e /(4N), where k is an integer, running from 0 N-1, representing a respective one of the N subbands;

B. a phase α

_k, such that α

₀ is equal to one of π

/4, 3π

/4, 5π

/4, and 7π

/4, and such that for two contiguous subbands represented by k and k-1, the difference α

_k -α

_k-1 is equal to one of π

/2 and -π

/2; and

C. a time delay τ

=(N_c -1)/(2f_e), where N_c is a number of coefficients required for realizing the prototype filter; and

b. a synthesizing filter bank for recoverying said incoming signal from said subband signals, said synthesizing filter bank comprising N prototype low-pass filters which are the same as the prototype filters used in the analyzing filter bank, except that the phase of the modulation signals is -α

_k,

whereby the number N is any integer greater than or equal to 2 and whereby N_c is not constrained to be a multiple of N.

2. A digital signal processing system comprising an analysing filter bank for dividing an incoming signal, sampled at a rate f_e and occupying a frequency band limmited to f_e /2, into N contiguous subband signals X_k (m) having respective bandwidths of f_e /2N and each being sampled at a rate of f_e /N, the analyzing filter bank comprising a polyphase network which comprises:

a. means for distributing N samples of the incoming signal over N branches in each period NT, with T=1/f_e ;

b. first means for calculating N signals P.sub.ρ

(m) from λ

consecutive signals entering the ρ

th branch and from a set of coefficients, said first calculating means having N inputs for receiving the samples from the distributing means, where ρ

is an integer varying from 0 to N-1, λ

is the integer part of (N-N_c +1)/N, and N_c is the number of coefficients in the set;

c. N second means for calculating a double-odd discrete cosine transform, each second calculating means having N inputs for receiving the signals P.sub.ρ

(m) and having an output at which a subband signal X_k (m) is supplied, said subband signal being formed according to the following formulae;

i. for λ

odd and for λ

even and N even;

##EQU39## ii. for λ

even and N odd;

##EQU40## whereby the analyzing filter bank filters an incoming signal according to a frequency response which is given by a succession of N elementary frequency responses, each of the N frequency responses having a shape which corresponds to a frequency response to a same prototype filter, which prototype filter is defined by the N_c coefficients and supplied with a modulation input for receiving a plurality of signals having respective frequencies and whereby N is any integer greater than or equal to two and whereby N_c is not constrained to be a multiple of N.

3. A system as claimed in claim 2, characterized in that first calculating means calculates each signal P.sub.ρ

(m) in accordance with the following formulae;

(a) for λ

even and N even;

##EQU41## h.sub.ρ

(r) representing λ

coefficients h(n) of the prototype filter for n=rN+ρ

, x.sub.ρ

(m-r) representing λ

samples entered into a branch ρ

of the polyphase network up to said period NT characterized by m.

4. The system of claim 2 or 3 comprising a synthesizing filter bank for recovering said incoming signal from said subband signals, the synthesizing bank comprising:

(a) N third means for calculating a double-odd discrete cosine transform, having N inputs for receiving the N subband signals X_k (m) and having N outputs at which N signals Y.sub.ρ

(m) are provided according to the following formulae;

for λ

odd and for λ

even and N even;

##EQU42## (b) a polyphase network having N inputs for receiving the signals Y.sub.ρ

(m) and comprising fourth means for calculating, at each period NT, indicated by m, and for each branch, indicated by ρ

, a signal x.sub.ρ

(m), from the coefficients of the prototype filter and from λ

consecutive samples of Y.sub.ρ

(m);

(c) means for time distributing the N samples of x.sub.ρ

(m) to produce a recovered input signal.

5. A system as claimed in claim 4, wherein the fourth calculating means calculates the signal x.sub.ρ

(m), in accordance with the following formulae;

(a) for λ

even and N even;

##EQU43## (b) for λ

even and N odd;

##EQU44## (c) for λ

odd;

##EQU45##