# inverse fourier transform of magnitude and phase

I stuck this question. Frequency response is written as magnitude and phase and I don't find inverse fourier given signal which as magnitude and phase.How can I solve it ? Can you explain the solution way in order? magnitude of signal is : y=−ω while −1≤ω<0, y=ω while 0≤ω<1 phase of signal is: y=−3ω

What is the Fourier transform? I mean I have phase and magnitude information of a signal that has been transformed from fourier. I want to find inverse fourier transform. And phase and magnitude information are above

• You had already asked this exact question before, deleted it, and posted it again here. Please don't do that. Rather, fix the issues with your original question.
– MBaz
Apr 2, 2020 at 22:26

You can express a complex signal $$y$$ as $$|y|.e^{i \phi_y}$$ where $$|y|$$ is the magnitude and $$\phi_y$$ is the phase. You can use Inverse the Fourier transform formula: $$\displaystyle y(t) = \frac{1}{2\pi}\int_{-\infty}^\infty Y(\omega) e^{j\omega t} d\omega$$ You can express $$Y(\omega)$$ in $$|y|.e^{i \phi_y}$$ form and then perform the IFFT. But I am not sure if a minus comes in magnitude unless its in dB.
What you have as the magnitude response is $$|Y(e^{j\omega})| = \left| \omega \right|$$, for $$\omega \in [-1,1]$$ and phase response is $$\angle{Y(e^{j\omega})} = -3\omega$$. So, $$Y(e^{j\omega}) = |Y(e^{j\omega})|. e^{j\angle{Y(e^{j\omega})} }$$.