Determine -3db gain on Freq- gain plot

Hello,

I got some freq-gain data from a filter and I am trying to determine -3db gain on the plot and get its frequency.

I am trying "interp1" but it comes with only one point.

How can I get the other one ?

Thank you

freq=t1.f;
noise=t1.noise;
gain=t1.gain;
figure
plot(freq,noise)
xlabel('Frequency')
ylabel('noise')
figure
[Max_gain,index1]=max(gain);
freq_max=freq(index1);
Gain_3db=Max_gain-3;
freq_3db=interp1(gain,freq,Gain_3db)
plot(freq,gain,'b')
ylabel('gain')
xlabel('Frequency')
hold on
plot(freq_3db,Gain_3db,'r*')

Answer 1

[Star Strider]

Use:

find(diff(sign(gain-Gain_3db)))

or something similar, to find the indices of all the points where the curve equals the specified value, then include a short range (I use [-1 0 1]) so that interp1 can interpolate over a limited set of values. This prevents problems with functions that can vary significantly, especially those that change frequently.

This approach works regardless of the number of times the transfer function equals the desired decibel value (so it would work for a filter with multiple passbands and stopbands), so long that at least one does.

I do not have your data, however this should work as an illustration —

freq = linspace(0, 10, 150).';                                  % Assuming Column Vectors
gain = mag2db(exp(-(freq-5).^2));                               % Create Function, Copnvert To 'dB'

[Max_gain,index1]=max(gain);
freq_max=freq(index1);
Gain_3db=Max_gain-3;

idxr = find(diff(sign(gain-Gain_3db)))+(-1:1)                   % Matrix Of Index Ranges

idxr = 2×3

65 66 67 83 84 85

for k = 1:size(idxr,1)
    freq_3db(k) = interp1(gain(idxr(k,:)),freq(idxr(k,:)),Gain_3db);
end

freq_3db                                                        % Desired Frequencies

freq_3db = 1×2

4.4121 5.5879

figure
hp1 = plot(freq, gain, 'DisplayName','Transfer Function');
hold on
hp2 = plot(freq_3db, Gain_3db, '+r', 'DisplayName','Transfer Function -3 dB Points');
hold off
grid
legend([hp1; hp2(1)], 'Location','best')
ylim([-20, 5])

Make appropriate changes to work with your data.

EDIT — (18 Nov 2022 at 13:15)

Clarified description. Code unchanged.

EDIT — (18 Nov 2022 at 19:48)

With the provided data —

freq = [2400        2470        2540        2610        2680        2750        2820        2890        2960        3030        3100        3170        3240        3310        3380        3450        3520        3590        3660        3730        3800        3870       3940        4010        4080        4150        4220        4290        4360        4430        4500        4570        4640    4710        4780        4850        4920        4990        5060        5130        5200];
gain = [-18.6680  -14.4060  -10.2174   -6.4374   -3.7861   -2.4066   -1.7975   -1.6368   -1.7193   -1.7336   -1.7873   -1.4274   -1.7189   -1.3573   -1.6372   -1.3042   -1.2758   -1.1481   -1.0076   -1.1632   -1.0454   -1.1071   -1.1686   -1.1704   -1.3548   -1.2611   -1.4895   -1.3286   -1.6556   -1.4886   -2.1840   -2.1738   -3.9351   -3.9649   -6.5240   -7.0555  -10.1172  -11.1532  -13.9887  -16.3625  -18.6674];

freq = freq(:);
gain = gain(:);

[Max_gain,index1]=max(gain);
freq_max=freq(index1);
Gain_3db=Max_gain-3;

idxr = find(diff(sign(gain-Gain_3db)))+(-1:1)                   % Matrix Of Index Ranges

idxr = 2×3

3 4 5 33 34 35

for k = 1:size(idxr,1)
    freq_3db(k) = interp1(gain(idxr(k,:)),freq(idxr(k,:)),Gain_3db);
end

fprintf('-3 dB Frequency = %.3f Hz\n',freq_3db)

-3 dB Frequency = 2674.152 Hz
-3 dB Frequency = 4711.168 Hz

% freq_3db                                                        % Desired Frequencies

figure
hp1 = plot(freq, gain, 'DisplayName','Transfer Function');
hold on
hp2 = plot(freq_3db, Gain_3db, '+r', 'DisplayName','Transfer Function -3 dB Points');
hold off
grid
legend([hp1; hp2(1)], 'Location','best')
ylim([-20, 5])
txtc = compose('  \\leftarrow %9.3f Hz',freq_3db);
text(freq_3db+15, [1 1]*Gain_3db, txtc, 'Horiz','left', 'Vert','middle', 'Rotation',-90)

Make appropriate changes to get different results.

.

[Moussa Ihab]

thank you

it works

[Star Strider]

As always, my pleasure!

Answer 2

[cr]

interp1() outputs linearly interpolated values that you are asking for. if Gain_3db is a scalar value the output is a scalar. The output you get this way gives you the freq at which gain fell by 3dB from its max value.

Perhaps the other value you are looking for is the start freq.

This is also not a great way to do what you seem to be looking for. It only works if gain values are monotonic.

Answer 3

[Askic V]

I think this code can help you, it is something I often use. It is not most efficient, but it works.

Please have a look at the example:

clear
clc
close all

num = 1;
den = [1 1];
g = tf(num,den);
[mag, phase, w] = bode(g);
magdb = squeeze(20*log10(mag));
semilogx(w,magdb);
ylim([-15, 0]);
grid on;
ind = find(magdb>=-3,1,'last');
% find two nearest points
P1w = [w(ind), w(ind+1)];
P2m = [magdb(ind), magdb(ind+1)];
% Find slope and intercept
c = [[1; 1]  P1w(:)]\P2m(:); 
% y = ax+b;
a = c(2);
b = c(1);
% Find angular frequency where magdb is -3 dB
w_3db = (-3-b)/a;
% Check if this is the case
mag_3db = a*w_3db+b;
hold on
plot(w_3db, mag_3db,'ro'); 
text(w_3db, mag_3db, [' -3 dB point,', newline, 'w = ', num2str(w_3db), 'rad/s'])

Answer 4

[Moussa Ihab]

Thanks for all answers you wrote.

I might have a small data which afftects plot and interceptions.

I have tried

freq_H=interp1(gain,freq,Gain_3db,)

freq_L=interp1(gain,freq,Gain_3db, 'previous')

and I got this

[Star Strider]

It would help to have your data. Please post the frequency and gain vectors.

Answer 5

[Moussa Ihab]

freq=

Columns 1 through 11

2400 2470 2540 2610 2680 2750 2820 2890 2960 3030 3100

Columns 12 through 22

3170 3240 3310 3380 3450 3520 3590 3660 3730 3800 3870

Columns 23 through 33

3940 4010 4080 4150 4220 4290 4360 4430 4500 4570 4640

Columns 34 through 41

4710 4780 4850 4920 4990 5060 5130 5200

gain=

Columns 1 through 13

-18.6680 -14.4060 -10.2174 -6.4374 -3.7861 -2.4066 -1.7975 -1.6368 -1.7193 -1.7336 -1.7873 -1.4274 -1.7189

Columns 14 through 26

-1.3573 -1.6372 -1.3042 -1.2758 -1.1481 -1.0076 -1.1632 -1.0454 -1.1071 -1.1686 -1.1704 -1.3548 -1.2611

Columns 27 through 39

-1.4895 -1.3286 -1.6556 -1.4886 -2.1840 -2.1738 -3.9351 -3.9649 -6.5240 -7.0555 -10.1172 -11.1532 -13.9887

Columns 40 through 41

-16.3625 -18.6674