Tham khảo tài liệu 'reviews of trading transaction timing_8', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | appendix four Frequency Response Characteristics of a Centered Moving Average Response Derivation Response Characteristics Application Implications Response of the Inverse Centered Moving Average In order to apply moving averages effectively the design parameters and response characteristics to be expected must be known. These are simply derived as follows RESPONSE DERIVATION 1. Defining e. as a cosinusoidal input to the averaging operation A cos cor 2. Determining eo - the output to be expected from the averaging operation under the assumption of centering and taking to at the mid-span point eữ A cos cor j4 cos co r r A cos co r r A cos co r 2rn A cos o r 2rn . A cos co r fu A cos co r - ị I Where n number of elements of the moving average tn digital data spacing of the data against which the average is applied. 3. This expression can be rewritten as follows eữ A cos cor 2A cos cor cos lX orrt 2A cos cor cos 2Xcorn . - . 2 4 cos cor cos 207 1 ì I 208 Appendix Four Ị ị 4. Factoring and combining terms I eữ ịA cos 1 2 cos 1 coi 2 cos 2Xwtft 2 cos - a tn I 5. Defining f cos lXwi cos 2X Xn cos n n -1 2 eo -TT- ei 0 n 1 6. And amplitude ratio is a 4 J where ei n f cos 1 cos 2X rn RESPONSE CHARACTERISTICS From the derivation we note the following Output is precisely in phase with input over the entire frequency range 0 GJ except for reversals of phase in the high attenuation areas . n tn is the span of the filter in units of time . The time lag is a constant L - units of time or one-half of the span. The cutoff frequency occurs when f Vi. or at a frequency _ 2tt co This frequency corresponds to a cutoff period of Tco ntn - span of the average The form of the amplitude response curve is a damped sinusoid but the major passband lobe repeats itself at frequency intervals of 2tf. This implies a first high frequency window that can induce frequency-folding effects at w 4 or at a frequency whose period is tn. The amplitude ratio of the first error lobe following cutoff .
