EURASIP Journal on Advances in Signal Processing

Table 2 Optimization results in terms of the number of basic logic elements (BLE) for the previous methods RPAG[9] using R iterations, a LUT MCM block[35] including pipelining and the proposed methods for optimal pipelined adder graphs using ILP Formulation 1 (Optimal PAG) and optimal pipelined adder/LUT graphs using ILP Formulation 2 (Optimal PALG), including the coefficients realized by LUTs (LUT Coeffs)

From: FIR filter optimization for video processing on FPGAs

				No. of BLE
Filter	Filter	B _c	B _x	RPAG[9]	RPAG[9]	LUT	Optimal	Optimal	LUT
type	size			( R = 1)	( R = 50)	MCM[35]	PAG	PALG	Coeffs
Gaussian	3 × 3	8	8	63	58	56	58	56	All
Gaussian	5 × 5	12	8	125	125	77	111	77	All
Laplacian	3 × 3	8	8	79	61	54	61	54	All
Unsharp	3 × 3	8	8	56	56	51	56	51	All
Unsharp	3 × 3	12	8	112	107	64	91	64	All
Lowpass	5 × 5	8	8	98	98	91	98	91	All
Lowpass	9 × 9	10	8	235	221	192	221	192	All
Lowpass	15 × 15	12	8	480	475	371	≤478	371	All
Highpass	5 × 5	8	8	74	74	69	74	69	All
Highpass	9 × 9	10	8	85	85	83	85	83	All
Highpass	15 × 15	12	8	186	186	170	186	170	All
Gaussian	3×3	8	10	73	68	71	68	68	None
Gaussian	5 × 5	12	10	145	143	98	129	98	All
Laplacian	3 × 3	8	10	93	71	69	71	68	All
Unsharp	3 × 3	8	10	66	66	66	66	66	None
Unsharp	3 × 3	12	10	130	123	80	105	80	All
Lowpass	5 × 5	8	10	114	114	118	114	112	33
Lowpass	9 × 9	10	10	271	255	276	255	254	117
Lowpass	15 × 15	12	10	550	543	546	≤547	≤545	None
Highpass	5 × 5	8	10	88	88	95	88	87	121
Highpass	9 × 9	10	10	101	101	115	101	101	None
Highpass	15 × 15	12	10	218	218	254	218	216	23
Gaussian	3 × 3	8	12	83	78	143	78	78	None
Gaussian	5 × 5	12	12	165	161	203	147	147	None
Laplacian	3 × 3	8	12	107	81	142	81	81	None
Unsharp	3 × 3	8	12	76	76	135	76	76	None
Unsharp	3 × 3	12	12	148	139	173	119	119	None
Lowpass	5 × 5	8	12	130	130	242	130	130	None
Lowpass	9 × 9	10	12	307	289	589	289	289	None
Lowpass	15 × 15	12	12	620	611	1203	≤620	≤620	None
Highpass	5 × 5	8	12	102	102	192	102	102	None
Highpass	9 × 9	10	12	117	117	232	117	117	None
Highpass	15 × 15	12	12	250	250	523	250	250	None
		Average:		168.09	162.73	207.36	160.3	150.97
	Improvement to RPAG (R = 50):			–	–	-27.43%	1.49%	7.23%

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