Question

Explain the differences and similarities of a trigonometric Fourier series and a Fourier transform of a square wave

Explain why Fourier transforms have negative frequency and the significance

Please be as detailed as possible for both points. Thank you

Answer 1

- Prigonometric fourier Series has the Coefficient which is composed of only its Odd hormonies Square ware fourier Coefficient fouriez tomsfoom of a Square - wave is composed of all frequency not only hormonien hus the inim Brigonometric fourier series of square ware ene discontinous where as fourier transform of square wire are Continous → fourier series is used to representa periodic function by a desirete sum of Complex exponential, while the fourtes

are the some except that p trom form can be lised to represent g. general, non periodic function by a Continuous. Superposition or integral of complex exponential in square ware signal is periodic so both the Pourier series and the fourier transform can be Calculated and they should tell us the some information The fourier Series Coefficient are Sin (KWOT) KA ourier trong form is 2 sin (KWOT) & (W-KW) k=-00 series loefficient and fourier transform. factor of 27 and im the frost case con plot bancs but in the second we mo K so the proportionality we in can have impulse

» fourier transform have negative frequency because it is given by X[w] = J xlta exp(-iwa) or 0 It is described by two special basis function called the complex exponential (CE). It takes two complex exponential to represent & Sinusoid one of a positive exponent and the other is negative exponent