Usually electronic band pass filters are set automatically to suppress signals(and noise!) from far outside the chosen spectral range. Really sharp edges are only possible with digital signal processing Characteristic for folded signals out of phase(but: phase error varies!) due to the band pass filter, signal intensity decreases with offset(of the unfolded signal) beyond the spectral width Fourier Transformation All periodic functions(e.g, of time t) can be described as a sum of sine and cosine functions f(t)=a,/2+ a, cos(t)+ a,cos( 2t)+ a, cos( 3t)+ b,sin(t)+b sin(2t)+ basin(3t)+ The coefficients an and bn can be calculated by fourier transformation F(o)=f(exp(ior dr with expiot=cos(ot)+ i sin(ot) F(o)-the FOURIER transform of f(t)-is a complex function that can be divided into a real and maginary part Re(F(O)=∫ f(t)cose(otdt Im(F(o)=f(t)sin(ot)dt16 Usually electronic band pass filters are set automatically to suppress signals (and noise!) from far outside the chosen spectral range. Really sharp edges are only possible with digital signal processing. Characteristic for folded signals: - out of phase (but: phase error varies!) - due to the band pass filter, signal intensity decreases with offset (of the unfolded signal) beyond the spectral width - Fourier Transformation All periodic functions (e.g., of time t) can be described as a sum of sine and cosine functions: f(t) = a0 / 2 + a1 cos(t) + a2 cos(2t) + a3 cos(3t) + ... + b1 sin(t) + b2 sin(2t) + b3 sin(3t) + ... The coefficients an and bn can be calculated by FOURIER transformation: F(w) = f (t)exp{iwt}dt -¥ +¥ ò with exp{iwt} = cos(wt) + i sin(wt) F(w) – the FOURIER transform of f(t) – is a complex function that can be divided into a real and an imaginary part: Re(F(w)) = õó -¥ +¥ f(t)cos(wt)dt Im(F(w)) = õó -¥ +¥ f(t)sin(wt)dt