Converting magnitude (dB) and phase (deg) to complex value

Let's assume I have magnitude value in dB and phase in degrees. How to change those to a complex number in Matlab?

Answer 1

[Star Strider]

Try this:

complexVector = [10.^(mag_dB/20) .* exp(1j*deg2rad(phase_degrees))]

or as an anonymous function:

complexVector = @(mag_dB,phase_degrees) [10.^(mag_dB/20) .* exp(1j*deg2rad(phase_degrees))]
Out = complexVector(mag_dB,phase_degrees)

also demonstrating how to call it.

EDIT — (19 Feb 2021 at 23:06)

Corrected typographical error.

[Mikael]

Here I have results: first inputs (freq, phase(deg) and magnitude(dB)) and then complex number calculated and printed like this:

fprintf(fid_xfile, '%12.0f \t %12.8f \t %12.8f \t %f%+fj\n', freqs(n), ...

(180/pi*(TF_freq_angle(n))), ...

(20*log10(abs(TF_freq(n)))), ...

[10.^(20*log10(abs(-6/20))), exp(1j*deg2rad(180/pi*(TF_freq_angle(n))))] );

Result:

freqs phase(deg) mag(dB) cplx result

0 0.00000000 -6.00 0.000000+1.000000j

250 -20.53069341 -6.00 0.000000+0.936484j

500 -44.68367392 -6.00 0.000000+0.711000j

I can't get it why I get always real part as 0.000000? -6dB here is artificially put there as whatever the value is there, result is 0.000000 + correct imaginary part.

[Star Strider]

I corrected the code a few minutes later.

See if the corrected code does what you want.

[Star Strider]

Mikael’s posted Answer is now this Comment —

Great, thanks. However I am not able to get good results, maybe my mistake. I have now tried older ("+") and new one (".*") with just some dB and deg value:

complexVector(n) = [10.^(20*log10(-6)/20) .* exp(1j*deg2rad(180/pi*(90)))];

% complexVector(n) = [10.^(20*log10(-6)/20) + exp(1j*deg2rad(180/pi*(90)))];

fprintf(fid_TF, '%12.0f \t %12.8f \t %12.8f \t %f%+fj\n', ...

freqs(n), ... %freq in degrees

(180/pi*(TF_freq_angle(n))), ... % angle in degrees

(20*log10(abs(TF_freq(n)))), ... % magnitude in dB

real(complexVector(n)), imag(complexVector(n)) ); % real and imaginary part of above

These both gives weird values - must be my mistake somewhere...:

2.688442-5.363980j

[Star Strider]

As always, my pleasure!

The problem is that this does the degrees-to-radians conversion twice:

complexVector(n) = [10.^(20*log10(-6)/20) .* exp(1j*deg2rad(180/pi*(90)))];
                                                       ↑       ↑

To illustrate:

complexVector = @(mag_dB,phase_degrees) [10.^(mag_dB/20) .* exp(1j*deg2rad(phase_degrees))];

mag_dB = 6:-3:-15;
phase_deg = -70:35:180;

Original = [mag_dB(:) phase_deg(:)]

Out = complexVector(mag_dB(:),phase_deg(:))

Check = [mag2db(abs(Out)) rad2deg(angle(Out))] 

producing:

Original =
     6   -70
     3   -35
     0     0
    -3    35
    -6    70
    -9   105
   -12   140
   -15   175


Out =
   0.6824 - 1.8749i
   1.1571 - 0.8102i
   1.0000 + 0.0000i
   0.5799 + 0.4061i
   0.1714 + 0.4710i
  -0.0918 + 0.3427i
  -0.1924 + 0.1615i
  -0.1772 + 0.0155i


Check =
    6.0000  -70.0000
    3.0000  -35.0000
         0         0
   -3.0000   35.0000
   -6.0000   70.0000
   -9.0000  105.0000
  -12.0000  140.0000
  -15.0000  175.0000

.

[Mikael]

Excellent, thank you! I appreciate your great help and example. One last final attempt is to get this complex Out vector printed out with fprintf... So far I am getting only real part visible.

[Star Strider]

As always, my pleasure!

Print the real and imag parts separately. Experiment with this:

Out = complexVector(mag_dB(:),phase_deg(:));

fprintf(1, '\t%9.6f%+8.6fj\n', [real(Out), imag(Out)].')

With the existing data in my earlier Comment, that produced:

	 0.682420-1.874933j
	 1.157083-0.810198j
	 1.000000+0.000000j
	 0.579915+0.406061j
	 0.171416+0.470962j
	-0.091832+0.342723j
	-0.192422+0.161461j
	-0.177151+0.015499j

.

[Mikael]

Awesome, thanks!

[Star Strider]

As always, my pleasure!