rcosfir.m
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上传日期:2013-03-02
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- function [bb, tim] = rcosfir(r, N_T, rate, T, fil_type, col)
- %RCOSFIR Design a raised cosine FIR filter.
- % B = RCOSFIR(R, N_T, RATE, T) designs and returns a raised cosine FIR filter.
- % A raised cosine filter is typically used to shape and oversample a symbol
- % stream before modulation/transmission as well as after reception and
- % demodulation. It is used to reduce the bandwidth of the oversampled symbol
- % stream without introducing intersymbol interference.
- %
- % The time response of the raised cosine filter is,
- %
- % h(t) = SINC(t/T) COS(pi R t/T)/(1 - 4 R^2 t^2 /T^2)
- %
- % The frequency domain has the spectrum
- %
- % / T when 0 < |f| < (1-r)/2/T
- % | pi T 1-R T 1-R 1+R
- % H(f) = < (1 + cos(----) (|f| - ----) --- when --- < |f| < ---
- % | r 2T 2 2 T 2 T
- % 0 when |f| > (1+r)/2/T
- %
- %
- % T is the input signal sampling period, in seconds. RATE is the
- % oversampling rate for the filter (or the number of output samples per input
- % sample). The rolloff factor, R, determines the width of the transition
- % band. R has no units. The transition band is (1-R)/(2*T) < |f| <
- % (1+R)/(2*T).
- %
- % N_T is a scalar or a vector of length 2. If N_T is specified as a
- % scalar, then the filter length is 2 * N_T + 1 input samples. If N_T is
- % a vector, it specifies the extent of the filter. In this case, the filter
- % length is N_T(2) - N_T(1) + 1 input samples (or
- % (N_T(2) - N_T(1))* RATE + 1 output samples).
- %
- % The default value for N_T is 3. The default value of RATE is 5.
- % The default value of T is 1.
- %
- % B = RCOSFIR(R, N_T, RATE, T, FILTER_TYPE) designs and returns a
- % square root raised cosine filter if FILTER_TYPE == 'sqrt'. The default
- % value of FILTER_TYPE, 'normal', returns a normal raised cosine filter.
- %
- % RCOSFIR(R, N_T, RATE, T, FILTER_TYPE, COL) produces the time response
- % and frequency response with the curve color as specified in the string
- % variable COL. The string in COL can be any type as defined in
- % PLOT. If COL is not present, the default color will be used in the plot
- %
- % [B, Sample_Time] = RCOSFIR(...) returns the FIR filter and the output sample
- % time for the filter. Note that the filter sample time is T / RATE.
- %
- % See also RCOSIIR, RCOSFLT, RCOSINE, FIRRCOS, RCOSDEMO.
- % Copyright 1996-2001 The MathWorks, Inc.
- % $Revision: 1.14 $
- %routine check
- if nargin < 1
- error('Not enough input variables for RCOSFIR')
- elseif nargin < 2
- N_T = [3 3]; rate = 5; T = 1; fil_type = 'normal';
- elseif nargin < 3,
- rate = 5; T = 1; fil_type = 'normal';
- elseif nargin < 4,
- T = 1; fil_type = 'normal';
- elseif nargin < 5,
- fil_type = 'normal';
- end;
- if (r < 0) | (r > 1) | ~isreal(r)
- error('The Rolloff factor in RCOSFIR must be a positive integer in the range, [0, 1].')
- end;
- [N_T, rate, T, fil_type] = checkinp(N_T, rate, T, fil_type,...
- [3 3], 5, 1, 'normal');
- if length(N_T) < 2
- N_T = [N_T N_T];
- end;
- if (rate <= 1) | (ceil(rate) ~= rate)
- error('RATE in RCOSFIR must be an integer greater than 1')
- end
- % calculation
- N_T(1) = -abs(N_T(1));
- time_T = [0 : 1/rate : max(N_T(2), abs(N_T(1)))];
- cal_time = time_T * T;
- time_T_r = r * time_T;
- if ~isempty(findstr(fil_type,'root')) | ~isempty(findstr(fil_type,'sqrt'))
- % square root raised cosine
- b=firrcos(rate*(N_T(2)-N_T(1)),1/(2*T),r,rate/T,'r','sqrt',-N_T(1)*rate)*sqrt(rate);
- else
- % regular raised cosine
- b=firrcos(rate*(N_T(2)-N_T(1)),1/(2*T),r,rate/T,'r',[],-N_T(1)*rate)*rate;
- end
- tim = cal_time(2) - cal_time(1);
- % In the case needs a plot
- if nargout < 1
- if nargin < 6
- col = '';
- end;
- % the time response part
- hand = subplot(211);
- % dont filter, plot using plot([0 : 1/rate : N_T(2) - N_T(1)],b) insteat
- out = filter(b, 1, [1, zeros(1, length(cal_time) - 1)]);
- plot(cal_time, out, col)
- % if not hold, change the axes
- hol = get(hand,'NextPlot');
- if (hol(1:2) ~= 'ad') | (max(get(hand,'Ylim')) < max(b))
- axis([min(cal_time), max(cal_time), min(out) * 1.1, max(out) * 1.1]);
- xlabel('time');
- title('Impulse Response of the Raised Cosine Filter (with time shift)')
- end;
- % the frequency response part
- hand = subplot(212);
- len = length(b);
- P = abs(fft(b)) * abs(N_T(2) - N_T(1)) / len * T;
- f = (0 : len / 2) / len * rate / T;
- ind = find(f < 1.5 / T);
- f = f(ind);
- P = P(ind);
- plot(f, P, col);
- hol = get(hand, 'NextPlot');
- if hol(1:2) ~= 'ad'
- xlabel('frequency');
- ylabel('Amplitude');
- title('Frequency Response of the Raised Cosine Filter')
- end;
- else
- bb = b;
- end;
- %--end of rcosfir.m--