# Noise reduction and square wave/sine function question

1. Dec 18, 2006

I have two simple questions but I'm not 100% on how to get the correct result.

1. "The noise is reduced by 6 dB" means its amplitude is cut to _%?
How is it calculated to 50%? I try 20log(Av)...

2. Does this wave contain 30k hertz sine function? (see attachment)
The answer is yes, but I try f=1/T, in this case T = 0.1 ms, so f is 10k, how is it 30k?

Thank you

#### Attached Files:

• ###### untitled1.bmp
File size:
27.5 KB
Views:
180
2. Dec 19, 2006

### Swapnil

Yes that is what you should try.
$$20 \log(A_v) = -6 \Rightarrow A_v = 10^\frac{-6}{20} \approx .50$$

You are right in saying that the frequency of your wave is 10kHz. However, I don't think that's what the question is asking. It is asking does this wave *contain* 30KHz sine function. That is, it asking if the fourier series of this wave includes a sine term that has the frequency 30kHz = 3(10kHz)? The answer is yes. Here is why: The given function is odd which means that only the coefficients b_k's are non-zero. The function is also half-wave symmetric which means that only the odd harmonics of b_k are non-zero. Thus, your fourier series should have the form:
$$f(t) = \sum_{k=1,3,5...}^{\infty} b_k \sin(k(10k)t)$$

Notice that one of the terms in the series is a sine term which has a frequency of 30kHz.

Last edited: Dec 19, 2006
3. Dec 19, 2006