-- Lowpass Digital Filter
--
-- Brian Edmonston, 1996
-- briane@qualcomm.com
--
-- lp_filter(t,RC,range,nsteps) lowpass
-- filters signal(t) using constant RC
--
-- Uses time domain convolution over 
-- nsteps within time span range. 
-- 
-- 
-- Use radians.  Very slow.  Shows need
-- for native powerPC capability.  
--
-- Selecting RC can be difficult in some cases.
--
-- For signals involving square waves,
-- using a  prime number for nsteps is best  

Xsteps = 700
Ysteps = 350
Xmin = 0; Xmax=4
Ymin = -5; Ymax = 5

-- ALL SINUSOID EXAMPLE

signal(t) = cos(t) + cos(5*t) + cos(50*t) + cos(500*t)

-- The example filter removes most of the 50/2pi and 500/2pi frequency 
-- signals, and produces a good copy of the 1/2pi and 5/2pi frequency
-- signals delayed by some small amount
 

lp_filter(t,RC,range,nsteps) = start := t-range,
  INC := range/nsteps,
  total:=sum(signal(start+i*INC)*exp(-RC*(t-(start+i*INC))),i,1,nsteps),
  total/nsteps

lp_filter_1(t,RC,range,nsteps) = start := t-range,
  INC := range/nsteps,
  total:=sum(signal_1(start+i*INC)*exp(-RC*(t-(start+i*INC))),i,1,nsteps),
  total/nsteps
                                                                                                                                           
plot signal(X)
plot cos(X) + cos(5*X)
plot lp_filter(X,1,.33,25)


-- DIGITAL TRANSMISSION

-- Data to be transmitted
DATA := { 1,-1, 1,-1,-1}:

-- BSPK modulated transmit signal
T(t) = DATA[trunc(t+1)]*sin(100*t)

-- Non-coherent mixing with carrier
-- signal at receive system

signal_1(t) = T(t)*sin(100*t + .1*2*pi) 

--  Plot receive signal and filtered 
--  and amplified receive signal
newaxis

plot signal_1(X)
plot 5*lp_filter_1(X,10,.05,31)