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We present a model based engineering approach to study raised cosine and tapered cosine windowed on/off keying to maximize power per bandwidth and minimize bandwidth. We also present a second example looking at raised cosine modulation and bandwidth. Raised cosine windowing functions have significantly better (faster) power spectral density convergence than on/off keying rectangular windowing functions. A rectangular windowing function has a higher average power compared to a tapered window. With practical constraints, what raised cosine or tapered cosine window provides the highest average power, and minimizes the bandwidth? Maximum average power occurs for a rectangular pulse. Minimum average power occurs for a raised cosine windowing function. Worst case (largest) bandwidth occurs for a pulse waveform. Best case (minimum) bandwidth occurs for a raised cosine window. For bandwidth comparison, half-cycle raised cosine modulation (Feher modulation) frequency shift keying compared to standard frequency shift keying uses 23% bandwidth at the 99 % power bandwidth points and it provides a 19 dB improvement (reduction) in power spectral density at fc ± 2fsym (center frequency ± 2 times the symbol frequency). On a dB scale, the power in a tapered cosine pulse is comparable to a rectangular pulse. A tapered cosine with widths of rise = 1/4 , top = 1/2 , and fall = 1/4 has 69% of the power (-1.6 dB) in a rectangular pulse. A tapered cosine with widths of rise = 1/3 , top = 1/3 , and fall = 1/3 has 46% of the power (-3.4 dB) in a rectangular pulse. A raised cosine pulse contains 37% of the power (-4.3 dB) in a rectangular pulse. Raised cosine (Feher) frequency shift keying (FSK) contains line spectra. We will show the line spectra are caused by a constant output from repeated symbols. We illustrate how a small dither removes the line spectra present in raised cosine (Feher) FSK.
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