I am a beginner in DSP but get confused when some formulas like below are referred:

cos(φt) · { A·cos(φt+Δ) } = ½·A·{ cos(Δ) + cos(2φt+Δ) } 
x(n) = Acos(ω0n+φ)
T= 2kπ/ω

The problem is that I do not know what terms like 'φ' or How T is equal to 2kπ/ω.

I know that I am lacking some elementary knowledge - but please let me know what are the topics / subjects I should hence first cover up such that when I read DSP related formulas, I understand them properly.

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    $\begingroup$ Maybe it's a good idea to start from some elementary book or doing online course in DSP instead of posting lot's of low-quality questions? $\endgroup$ – jojek Jul 3 '14 at 6:51
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    $\begingroup$ The formula that you have shown here has little to do with DSP but is a basic trigonometric identity. DSP is a fairly math intensive topic and it maybe a good idea brush up on Algebra and Calculus before diving in. You should at least be comfortable with complex numbers and phasor math, which are essential to DSP $\endgroup$ – Hilmar Jul 3 '14 at 12:02
  • $\begingroup$ Personally I feel no question is of low-quality as long as it clarifies one's doubt. Thanks for your valuable comment. I would start with Trig, Algebra, Calculus, Complex Numbers and Phasor Mathematics $\endgroup$ – Programmer Jul 3 '14 at 13:05

First, the formulas by itself are from sine/cosine waves, so you should read a little about them first. Here.

For the rest, you only have to keep in mind the unities $\phi$ in $\frac{rad}{s}$, $\Delta$ in $rad$ and finally in x(n) is a discrete sine-wave (or sampled) that is why the $n$ in the formula. It is basically the same thing as with the $t$ but in discrete, or sampled, time.

The $T$ stands for the Period of the wave. You can perform simply math there to check the following:

$$ T = \frac{2k\pi}{\omega} $$ $$ T = \frac{1}{f} $$ $$ \omega = 2\pi f= \frac{2\pi}{T} $$

Then you seen why we can obtain:

$$ T = \frac{2\pi}{\omega} $$

Finally, the $k$ stands, normally, for each of the cycle the wave is repeated. Then you can have $k$ = 0, 1, 2, ..., N

To understand more how to work with this on DPS you only should read about Sine-waves and its representation. Basic knowledge in shifting and characteristics as Period, Frequency, Angular velocity and phase is a must.


  • $\begingroup$ Thanks for the explanation, it gives me a good insight of how to approach to self educate DSP. Thanks a lot $\endgroup$ – Programmer Jul 3 '14 at 13:04

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