ECE 4710: Lecture #16 1 Bandpass Spectrum  Spectrum of bandpass signal is directly related to spectrum of complex envelope  We have already shown that f f c -B f c f c +B -f c -B - f c - f c +B -B 0 +B f

ECE 4710: Lecture #16 2 Bandpass PSD  PSD of bandpass signal is  Derivation is in book but this is intuitively correct since FT  V/Hz so that PSD  | FT | 2  W/Hz  Average normalized power of bandpass waveform is  Bandpass power found from baseband signal representation g(t) if desired, otherwise from PSD

ECE 4710: Lecture #16 3 Peak Envelope Power  Peak Envelope Power (PEP) is the average power that would be obtained if | g(t) | were held constant at its peak value  Useful measure of power for high power Tx specifications »AM Broadcast Radio, TV, etc.  Transmitters must be able to handle instantaneous signal power, e.g. peak, without saturating or being damaged »Average power does not provide any measure of what the worst- case peak power may be  PEP given by

ECE 4710: Lecture #16 4 AM Signal  General meaning of amplitude modulation  the time variation of the amplitude of the carrier signal contains/represents the source information signal m(t)  There are many types that meet the general definition  Amplitude Modulated (AM) signal is a specific case of the general class of amplitude modulated signals where  This is used for AM broadcast radio and is also called Double Side Band – Large Carrier  DSB-LC

ECE 4710: Lecture #16 5 AM Signal  AM Baseband Signal   AM Bandpass Signal   AM signal g(t) is purely real since m(t) only represents amplitude information so  Using Euler’s Identity   So

ECE 4710: Lecture #16 6 AM Signal Spectrum  AM Baseband Spectrum  Table 2-2, pg. 64 : 1   (f) so  A c represents DC power and constant carrier such that even if m(t) = 0 the carrier signal s(t) = A c cos 2  f c t is always present  DSB-LC -B 0 +B f 0 f f

ECE 4710: Lecture #16 7 AM Signal Spectrum  AM Bandpass Spectrum  LSB + USB = DSB LC

ECE 4710: Lecture #16 8 AM Signal Power  Using baseband signal g(t)  If DC power in source waveform m(t) is zero then 2  m(t)  = 0  No delta function in M(f )  Signal power is “wasted” on carrier  does not contribute to S/N at Rx of the recovered information waveform  LC enables extremely simple Rx circuit but AM is power ineffecient

ECE 4710: Lecture #16 9 Communication System Goal: Design system to transmit information, m(t), with as little deterioration as possible within design constraints of signal power, signal bandwidth, and system cost ˜ Information Source Baseband Signal Processing Modulation & Carrier Circuits Transmission Channel Demodulation & Carrier Circuits Baseband Signal Processing Information Sink Noise n (t) m (t) s (t) r (t) m (t) Transmitter (Tx)Receiver (Rx)

ECE 4710: Lecture #16 10 Rx S+N  Model for received signal plus noise  s(t) is signal out of transmitter »Spectral response may be modified by channel »Noise added in channel  Thus the signal at Rx input is  If channel is distortion free (a big IF!!) then »Constant amplitude ( A ) and linear phase (2  f T g )

ECE 4710: Lecture #16 11 Rx S+N  Distortion free received signal + noise is  T g and   ( f c ) must be estimated by Rx for digital signals  Accomplished by bit synchronizer for digital signals  Not necessarily required for analog signals (e.g. AM)

ECE 4710: Lecture #16 12 Rx S+N  A high performance Rx is designed to correct for  Channel attenuation  amplify signal  Channel delay  synchronization circuits  Channel frequency distortion  equalizing filter  If channel effects are largely corrected then  Uncompensated effects of channel spectral response can be included in g(t) if needed  This is a best-case approach and is not valid for some applications  wireless mobile radio

ECE 4710: Lecture #16 13 Analog Filters  Filters modify the spectral characteristics of an input signal to produce desired output signal  Variety of needs and applications  Pulse shaping for minimizing BW  Correcting for distortion caused by channel  Selection of desired signals from specific frequencies  Rejection of undesired signals and noise outside of desired signal BW  Filters classified by type of construction (LC, SAW, etc.) and by spectral response characteristics (Butterworth, Chebyshev, etc.)  Elements used to construct filter should have high Q

ECE 4710: Lecture #16 14 Analog Filters  Two Q types to describe filter quality  Energy Storage Q  »LC circuit elements are imperfect and have some resistance which leads to energy dissipation via heat »Desire high Q for individual circuit elements  Frequency Selective Q  »f o is resonant frequency (design center frequency) & B is 3-dB BW »Measure of the filter’s overall ability to select desired frequency band »Higher selectivity means narrower band filter on a % basis

ECE 4710: Lecture #16 15 Analog Filter Types

ECE 4710: Lecture #16 16 Analog Filter Types

ECE 4710: Lecture #16 17 Filter Responses  Butterworth  Maximally flat response in passband  Modest rolloff for attenuation response  Chebyshev  Sharpest rolloff for minimum number of circuit elements  1-3 dB amplitude variation in passband  ripple  Bessel  Linear phase response in passband  Distortion-free filter to preserve pulse shape  Raised Cosine  Pulse shaping to minimize signal BW and no ISI