## Why downsampling with sine and cosine

Started by 7 years ago4 replieslatest reply 6 years ago534 views

Hi there,

First of all: Hello DSP related forum! I am working in a FPGA design service company and digging deeper and deeper into the world of DSP. Therefore, I'm happy to have found this forum and will tumble in with my first question right away.

Let's say we have a 77Ghz sine wave that we downsample with 70GHz. Usually this is done by multiplying the incoming signal with a sine and a cosine wave of 70GH. In case of an amplitude and phase modulated digital signal (QAM etc.) it's completely clear why this is necessary but if I just have a radar signal for i.e. object recognition or distance messurement than why would I need that? Doesn't hold the signal which results from the downsampling only with the 70GHz sine wave already all relevant information (correct amplitude and phase alignment of the incoming 77GHz wave?). If I compare the spectrum of sine(77GHz)*sine(70GHz) to sine(77GHz)*sine(70GHz)+i*sine(77GHz)*cos(70GHz) than all I notice is that the mirrored images above pi are gone but what does that tell me?

I'd be very happy if somebody could solve the knot in my brain or point me to some website, book and chapter where that holds the answer.

Lennart

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Sorry, a clarification: Are you perhaps referring to "undersampling" instead of "downsampling"?

As far as I know, downsampling is the process of reducing the sampling rate of an (already sampled) signal, and I find quite strange having a signal sampled at 2x77GHz.

Also the term "we downsample with 70GHz" suggests me that you are in fact mixing (analogically) the 77GHz signal with another of 70GHz to get a result of 7GHz which you can eventually digitalize to apply your DSP algorithms.

Please forgive me if I'm asking stupid questions, but I couldn't make myself a mental map of your problem.

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Hi,

First, lets fix some terms. The process of converting a signal to a lower frequency is named as downconversion. So, you downconvert you signal, initially centered at 77 GHz, to the intermediate frequency of 7 GHz.

Have you thought about what happen with the noise or any other interference signal present in the frequency of 63 GHz? This is your image frequency. 63-70 = -7 GHz.

Using a quadrature downconverter, the signals at your image frequency will not overlap with your main signal at the downconverter output, because the signal is complex. On the other hand, if you do not use a quadrature downconverter, the overlapping will happen. In this case, the solution is filter out your image frequency before the  downconversion, without filtering out your main signal. This may be difficult to achieve if your image frequency is close to your main signal frequency.

Regards

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