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Digital Down-Conversion (Phase Computation)

In digital signal processing, the digital down converter (DDC) downconverts the input signal by multiplying it with a complex exponential that has the specified center frequency.

The purpose is to create a subVI that performs digital down-conversion based on basic mixing equation using Euler's formula.

The input 'x(t)' is a complex signal with some center frequency 'fc'.

Basic mixing equation is to multiply input with complex exponential. 
y(t) = x(t) * exp (-jwt+phi)

where x(t) = I + j Q,  w = 2*pi*fc*t and phi is the initial phase value.

Now, the question is how to compute this phase value for continuous processing. The only information present is the input signal and center frequency. Normally, this phase value is computed based on current iteration and fed back to input for next iteration. I have tried to compute using atan(Q/I) but didn't get the required results. 

Kind assistance is required in this regard.

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